111:@0.890754:0.963104:0.932133:0.963104:0.932133:0.941283:0.890754:0.941283:0.000000:0.000000:0.000000
Matemática:@0.795130:0.956142:0.879896:0.956142:0.879896:0.943479:0.795130:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
10.º EGB:@0.820728:0.967458:0.879897:0.967458:0.879897:0.954794:0.820728:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DUA:@0.748004:0.068322:0.791647:0.068322:0.791647:0.048070:0.748004:0.048070:0.000000:0.000000:0.000000
. Representación:@0.791647:0.067693:0.923937:0.067693:0.923937:0.050792:0.791647:0.050792:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Método por completar el trinomio cuadrado perfecto:@0.096359:0.101664:0.556767:0.101664:0.556767:0.083227:0.096359:0.083227:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Existen expresiones algebraicas que no pueden ser factorizadas fácilmente. En estos :@0.096359:0.132201:0.716501:0.132201:0.716501:0.115813:0.096359:0.115813:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
casos podemos encontrar las raíces completando trinomios cuadrados perfectos. Se :@0.096359:0.148798:0.716541:0.148798:0.716541:0.132409:0.096359:0.132409:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
transforman ecuaciones cuadráticas de la forma :@0.096359:0.165394:0.462500:0.165394:0.462500:0.149005:0.096359:0.149005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax:@0.464858:0.165394:0.481591:0.165394:0.481591:0.150001:0.464858:0.150001:0.000000:0.000000
2 + :@0.481591:0.165394:0.508265:0.165394:0.508265:0.149005:0.481591:0.149005:0.000000:0.000000:0.000000:0.000000
bx:@0.510612:0.165394:0.527179:0.165394:0.527179:0.150001:0.510612:0.150001:0.000000:0.000000
 +   = 0 en un trinomio :@0.527179:0.165394:0.716547:0.165394:0.716547:0.149005:0.527179:0.149005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.550932:0.165394:0.558598:0.165394:0.558598:0.150001:0.550932:0.150001:0.000000
cuadrado perfecto. Para ello, se verifica que el coeficiente de 2 sea uno (  = 1). :@0.096359:0.181991:0.716447:0.181991:0.716447:0.165602:0.096359:0.165602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 x :@0.560218:0.181991:0.576397:0.181991:0.576397:0.166597:0.560218:0.166597:0.000000:0.000000:0.000000
a:@0.661957:0.181991:0.671226:0.181991:0.671226:0.166597:0.661957:0.166597:0.000000
Luego, se suma a los dos miembros de la ecuación la expresión: :@0.096359:0.211007:0.566146:0.211007:0.566146:0.194618:0.096359:0.194618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.575552:0.203650:0.585724:0.203650:0.590944:0.187980:0.580772:0.187980:0.000000
2:@0.578431:0.222981:0.587424:0.222981:0.587424:0.207311:0.578431:0.207311:0.000000
2:@0.597172:0.193985:0.602384:0.193985:0.602384:0.184904:0.597172:0.184904:0.000000
Ejemplos:@0.096359:0.238290:0.162828:0.238290:0.162828:0.221652:0.096359:0.221652:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a):@0.096359:0.268053:0.111267:0.268053:0.111267:0.251152:0.096359:0.251152:0.000000:0.000000
Resuelve la ecuación 2 2 – 8  + 3 = 0 por el método de completar T.C.P.:@0.120094:0.268053:0.638169:0.268053:0.638169:0.251664:0.120094:0.251664:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.285501:0.268053:0.292964:0.268053:0.292964:0.252660:0.285501:0.252660:0.000000
x:@0.324512:0.268053:0.331975:0.268053:0.331975:0.252660:0.324512:0.252660:0.000000
Dividimos toda la ecuación para 2: :@0.120094:0.300900:0.375555:0.300900:0.375555:0.284511:0.120094:0.284511:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.398282:0.301252:0.408399:0.301252:0.408399:0.285679:0.398282:0.285679:0.000000
= −:@0.434769:0.301252:0.458651:0.301252:0.458651:0.285679:0.434769:0.285679:0.000000:0.000000:0.000000
x:@0.379634:0.300574:0.387097:0.300574:0.387097:0.285181:0.379634:0.285181:0.000000
x:@0.422883:0.300574:0.430346:0.300574:0.430346:0.285181:0.422883:0.285181:0.000000
4:@0.411882:0.300574:0.420875:0.300574:0.420875:0.284185:0.411882:0.284185:0.000000
3:@0.462042:0.291612:0.471035:0.291612:0.471035:0.275223:0.462042:0.275223:0.000000
2:@0.461836:0.311065:0.470829:0.311065:0.470829:0.294676:0.461836:0.294676:0.000000
2:@0.388754:0.292913:0.393965:0.292913:0.393965:0.283415:0.388754:0.283415:0.000000
Tomamos el coeficiente de  , dividimos para 2 y elevamos al cuadrado. :@0.120102:0.328178:0.641066:0.328178:0.641066:0.311789:0.120102:0.311789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.321479:0.328178:0.328943:0.328178:0.328943:0.312785:0.321479:0.312785:0.000000
4 ÷ 2 = 2;  22 = 4:@0.356971:0.351897:0.475645:0.351897:0.475645:0.335508:0.356971:0.335508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sumamos el valor de 4 a los dos miembros de la ecuación::@0.120102:0.375616:0.546903:0.375616:0.546903:0.359227:0.120102:0.359227:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.363638:0.415958:0.373755:0.415958:0.373755:0.400385:0.363638:0.400385:0.000000
+ =− +:@0.399609:0.415958:0.475844:0.415958:0.475844:0.400385:0.399609:0.400385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.345008:0.415280:0.352471:0.415280:0.352471:0.399887:0.345008:0.399887:0.000000
x:@0.388258:0.415280:0.395721:0.415280:0.395721:0.399887:0.388258:0.399887:0.000000
4:@0.377256:0.415280:0.386249:0.415280:0.386249:0.398891:0.377256:0.398891:0.000000
4:@0.413227:0.415280:0.422220:0.415280:0.422220:0.398891:0.413227:0.398891:0.000000
3:@0.453105:0.406318:0.462097:0.406318:0.462097:0.389929:0.453105:0.389929:0.000000
2:@0.452897:0.425771:0.461890:0.425771:0.461890:0.409382:0.452897:0.409382:0.000000
4:@0.479334:0.415280:0.488327:0.415280:0.488327:0.398891:0.479334:0.398891:0.000000
2:@0.354110:0.407618:0.359321:0.407618:0.359321:0.398120:0.354110:0.398120:0.000000
Factorizamos el trinomio cuadrado perfecto del primer miembro y reducimos :@0.120102:0.449270:0.716542:0.449270:0.716542:0.432881:0.120102:0.432881:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
términos: :@0.120102:0.473611:0.192928:0.473611:0.192928:0.457223:0.120102:0.457223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.195545:0.474704:0.201681:0.474704:0.201681:0.454771:0.195545:0.454771:0.000000
):@0.237634:0.474704:0.243770:0.474704:0.243770:0.454771:0.237634:0.454771:0.000000
−:@0.215596:0.472250:0.225713:0.472250:0.225713:0.456677:0.215596:0.456677:0.000000
=:@0.254552:0.472250:0.264669:0.472250:0.264669:0.456677:0.254552:0.456677:0.000000
x:@0.201336:0.471572:0.209242:0.471572:0.214046:0.455183:0.206140:0.455183:0.000000
2:@0.228473:0.471572:0.237466:0.471572:0.237466:0.455183:0.228473:0.455183:0.000000
5:@0.267999:0.463046:0.276992:0.463046:0.276992:0.446657:0.267999:0.446657:0.000000
2:@0.267790:0.482535:0.276782:0.482535:0.276782:0.466146:0.267790:0.466146:0.000000
2:@0.244021:0.462025:0.249233:0.462025:0.249233:0.452527:0.244021:0.452527:0.000000
Sacamos la raíz cuadrada a los dos miembros de la ecuación: :@0.120102:0.509605:0.567910:0.509605:0.567910:0.493217:0.120102:0.493217:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.570172:0.509007:0.578077:0.509007:0.582882:0.492618:0.574976:0.492618:0.000000
2:@0.595843:0.509007:0.604836:0.509007:0.604836:0.492618:0.595843:0.492618:0.000000
5:@0.646999:0.500488:0.655991:0.500488:0.655991:0.484099:0.646999:0.484099:0.000000
2:@0.646796:0.519933:0.655788:0.519933:0.655788:0.503544:0.646796:0.503544:0.000000
−= ±:@0.583718:0.509685:0.630801:0.509685:0.630801:0.494112:0.583718:0.494112:0.000000:0.000000:0.000000:0.000000
Finalmente, obtenemos las soluciones: :@0.120134:0.551922:0.407050:0.551922:0.407050:0.535534:0.120134:0.535534:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.409741:0.552012:0.417266:0.552012:0.421816:0.536490:0.414291:0.536490:0.000000
y x:@0.501811:0.552012:0.530761:0.552012:0.535310:0.536490:0.506361:0.536490:0.000000:0.000000:0.000000
2:@0.443016:0.552012:0.452084:0.552012:0.452084:0.535486:0.443016:0.535486:0.000000
5:@0.479807:0.543379:0.488875:0.543379:0.488875:0.526854:0.479807:0.526854:0.000000
2:@0.479599:0.563066:0.488666:0.563066:0.488666:0.546540:0.479599:0.546540:0.000000
... ...:@0.491000:0.552012:0.522960:0.552012:0.522960:0.535486:0.491000:0.535486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2–:@0.557354:0.552012:0.577886:0.552012:0.577886:0.535486:0.557354:0.535486:0.000000:0.000000
5:@0.594516:0.543379:0.603584:0.543379:0.603584:0.526854:0.594516:0.526854:0.000000
2:@0.594306:0.563066:0.603373:0.563066:0.603373:0.546540:0.594306:0.546540:0.000000
2:@0.533811:0.554032:0.539066:0.554032:0.539066:0.544455:0.533811:0.544455:0.000000
1:@0.420793:0.551764:0.424579:0.551764:0.424579:0.544863:0.420793:0.544863:0.000000
=+:@0.429820:0.552695:0.463676:0.552695:0.463676:0.536992:0.429820:0.536992:0.000000:0.000000
=:@0.544151:0.552695:0.554352:0.552695:0.554352:0.536992:0.544151:0.536992:0.000000
b):@0.096359:0.599375:0.112576:0.599375:0.112576:0.582475:0.096359:0.582475:0.000000:0.000000
Hallar las raíces de la ecuación:  2 – 6  + 8 = 0.:@0.120094:0.599375:0.457320:0.599375:0.457320:0.582987:0.120094:0.582987:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.348228:0.599375:0.359008:0.599375:0.359008:0.583982:0.348228:0.583982:0.000000:0.000000
x:@0.390557:0.599375:0.398020:0.599375:0.398020:0.583982:0.390557:0.583982:0.000000
Primero: se resta 8 en ambos lados de la igualdad.:@0.120094:0.623094:0.483557:0.623094:0.483557:0.606706:0.120094:0.606706:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En este caso, no se divide para a, porque a = 1.:@0.120094:0.646813:0.459308:0.646813:0.459308:0.630425:0.120094:0.630425:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.120103:0.670532:0.127566:0.670532:0.127566:0.655139:0.120103:0.655139:0.000000
2 – 6  + 8 – 8 = 0 – 8  :@0.127566:0.670532:0.281323:0.670532:0.281323:0.654144:0.127566:0.654144:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.159115:0.670532:0.166578:0.670532:0.166578:0.655139:0.159115:0.655139:0.000000
  2 – 6  = – 8:@0.337595:0.670532:0.429402:0.670532:0.429402:0.654144:0.337595:0.654144:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.341631:0.670532:0.349094:0.670532:0.349094:0.655139:0.341631:0.655139:0.000000
x:@0.380642:0.670532:0.388106:0.670532:0.388106:0.655139:0.380642:0.655139:0.000000
Segundo: se suma :@0.120094:0.706394:0.258430:0.706394:0.258430:0.690006:0.120094:0.690006:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.271569:0.697280:0.280838:0.697280:0.280838:0.680919:0.271569:0.680919:0.000000
2:@0.271090:0.716615:0.280083:0.716615:0.280083:0.700226:0.271090:0.700226:0.000000
2:@0.295339:0.687908:0.300551:0.687908:0.300551:0.678410:0.295339:0.678410:0.000000
en ambos lados, y se realiza la potencia. :@0.310369:0.706410:0.604047:0.706410:0.604047:0.690021:0.310369:0.690021:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.124195:0.748689:0.131658:0.748689:0.131658:0.733296:0.124195:0.733296:0.000000
2:@0.133295:0.741027:0.138506:0.741027:0.138506:0.731945:0.133295:0.731945:0.000000
6:@0.155336:0.748689:0.164328:0.748689:0.164328:0.733019:0.155336:0.733019:0.000000
x:@0.165969:0.748689:0.173432:0.748689:0.173432:0.733296:0.165969:0.733296:0.000000
+:@0.177007:0.749366:0.187123:0.749366:0.187123:0.733794:0.177007:0.733794:0.000000
6:@0.212922:0.739808:0.221915:0.739808:0.221915:0.724139:0.212922:0.724139:0.000000
2:@0.212922:0.759143:0.221915:0.759143:0.221915:0.743474:0.212922:0.743474:0.000000
2:@0.233390:0.730419:0.238602:0.730419:0.238602:0.721337:0.233390:0.721337:0.000000
=:@0.243232:0.749366:0.253349:0.749366:0.253349:0.733794:0.243232:0.733794:0.000000
8:@0.266843:0.748689:0.275836:0.748689:0.275836:0.733019:0.266843:0.733019:0.000000
+:@0.278250:0.749366:0.288367:0.749366:0.288367:0.733794:0.278250:0.733794:0.000000
6:@0.314169:0.739808:0.323161:0.739808:0.323161:0.724139:0.314169:0.724139:0.000000
2:@0.314169:0.759143:0.323161:0.759143:0.323161:0.743474:0.314169:0.743474:0.000000
2:@0.334638:0.730419:0.339850:0.730419:0.339850:0.721337:0.334638:0.721337:0.000000
x:@0.401933:0.746404:0.409396:0.746404:0.409396:0.731011:0.401933:0.731011:0.000000
2 – 6  + 9 = – 8 + 9 :@0.409396:0.746404:0.549833:0.746404:0.549833:0.730015:0.409396:0.730015:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.440944:0.746404:0.448407:0.746404:0.448407:0.731011:0.440944:0.731011:0.000000
    2 – 6  + 9 = 1 :@0.578825:0.746404:0.700853:0.746404:0.700853:0.730015:0.578825:0.730015:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 x:@0.590932:0.746404:0.601712:0.746404:0.601712:0.731011:0.590932:0.731011:0.000000:0.000000
x:@0.633260:0.746404:0.640724:0.746404:0.640724:0.731011:0.633260:0.731011:0.000000
Tercero: se factoriza: (  – 3)2 = 1 :@0.120100:0.786720:0.351218:0.786720:0.351218:0.770331:0.120100:0.770331:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.275241:0.786720:0.282704:0.786720:0.282704:0.771326:0.275241:0.771326:0.000000
Cuarto: se obtiene la solución. :@0.120100:0.811670:0.343996:0.811670:0.343996:0.795281:0.120100:0.795281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.348077:0.812439:0.355540:0.812439:0.355540:0.797046:0.348077:0.797046:0.000000
3:@0.371688:0.812439:0.380681:0.812439:0.380681:0.796769:0.371688:0.796769:0.000000
= ±:@0.383039:0.813117:0.407180:0.813117:0.407180:0.797544:0.383039:0.797544:0.000000:0.000000:0.000000
1:@0.419102:0.812439:0.428095:0.812439:0.428095:0.796769:0.419102:0.796769:0.000000
   Entonces:  ₁ = 4 y   = 2:@0.429432:0.811681:0.612849:0.811681:0.612849:0.795292:0.429432:0.795292:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.516539:0.811681:0.524002:0.811681:0.524002:0.796288:0.516539:0.796288:0.000000
x:@0.572099:0.811681:0.579562:0.811681:0.579562:0.796288:0.572099:0.796288:0.000000
2:@0.579558:0.814845:0.584801:0.814845:0.584801:0.805290:0.579558:0.805290:0.000000
Quinto: se verifican las soluciones: :@0.120112:0.835400:0.372551:0.835400:0.372551:0.819011:0.120112:0.819011:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.127056:0.866761:0.133841:0.866761:0.133841:0.852767:0.127056:0.852767:0.000000
2 – 6  + 8 = 0:@0.133841:0.866761:0.220300:0.866761:0.220300:0.851862:0.133841:0.851862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.162521:0.866761:0.169306:0.866761:0.169306:0.852767:0.162521:0.852767:0.000000
(4)2 – 6(4) + 8 = 0:@0.127056:0.881848:0.240838:0.881848:0.240838:0.866949:0.127056:0.866949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0 = 0:@0.127056:0.896936:0.160728:0.896936:0.160728:0.882037:0.127056:0.882037:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.291364:0.866761:0.298148:0.866761:0.298148:0.852767:0.291364:0.852767:0.000000
2 – 6  + 8 = 0:@0.298148:0.866761:0.384607:0.866761:0.384607:0.851862:0.298148:0.851862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.326828:0.866761:0.333613:0.866761:0.333613:0.852767:0.326828:0.852767:0.000000
(2)2 – 6(2) + 8 = 0:@0.291364:0.881848:0.405146:0.881848:0.405146:0.866949:0.291364:0.866949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0 = 0:@0.291364:0.896936:0.325036:0.896936:0.325036:0.882037:0.291364:0.882037:0.000000:0.000000:0.000000:0.000000:0.000000
Las dos soluciones satisfacen a la :@0.447570:0.874336:0.709574:0.874336:0.709574:0.857947:0.447570:0.857947:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ecuación cuadrática.:@0.447570:0.890932:0.598197:0.890932:0.598197:0.874543:0.447570:0.874543:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad:@0.750200:0.108682:0.907406:0.108682:0.907406:0.091782:0.750200:0.091782:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática e Historia:@0.755005:0.138233:0.912777:0.138233:0.912777:0.122868:0.755005:0.122868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
François Viète :@0.755005:0.156878:0.849855:0.156878:0.849855:0.141979:0.755005:0.141979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(1540 - 1603, Francia):@0.755005:0.171966:0.895539:0.171966:0.895539:0.157067:0.755005:0.157067:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Fue un matemático :@0.755005:0.330184:0.888905:0.330184:0.888905:0.315285:0.755005:0.315285:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
francés que consideró las :@0.755005:0.345271:0.926966:0.345271:0.926966:0.330372:0.755005:0.330372:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ecuaciones cuadráticas de :@0.755005:0.360359:0.934222:0.360359:0.934222:0.345460:0.755005:0.345460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la manera general, :@0.755005:0.375446:0.881316:0.375446:0.881316:0.360547:0.755005:0.360547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax :@0.755005:0.390534:0.773231:0.390534:0.773231:0.376540:0.755005:0.376540:0.000000:0.000000:0.000000
2 +   +   = 0, donde :@0.773231:0.390534:0.914688:0.390534:0.914688:0.375635:0.773231:0.375635:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bx:@0.795344:0.390534:0.810405:0.390534:0.810405:0.376540:0.795344:0.376540:0.000000:0.000000
c:@0.827727:0.390534:0.834696:0.390534:0.834696:0.376540:0.827727:0.376540:0.000000
a b c:@0.755005:0.405622:0.800119:0.405622:0.800119:0.391628:0.755005:0.391628:0.000000:0.000000:0.000000:0.000000:0.000000
,   y   son cantidades :@0.763431:0.405622:0.908205:0.405622:0.908205:0.390723:0.763431:0.390723:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conocidas. Gracias a esto, :@0.755005:0.420709:0.927033:0.420709:0.927033:0.405810:0.755005:0.405810:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es posible escribir la :@0.755005:0.435797:0.892138:0.435797:0.892138:0.420898:0.755005:0.420898:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fórmula cuadrática para :@0.755005:0.450884:0.916682:0.450884:0.916682:0.435985:0.755005:0.435985:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
resolver ecuaciones de :@0.755005:0.465972:0.910701:0.465972:0.910701:0.451073:0.755005:0.451073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
este tipo.:@0.755005:0.481060:0.815697:0.481060:0.815697:0.466161:0.755005:0.466161:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Indaga sobre François :@0.755005:0.499705:0.897113:0.499705:0.897113:0.485712:0.755005:0.485712:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Viète y elabora una :@0.755005:0.514793:0.878887:0.514793:0.878887:0.500799:0.755005:0.500799:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
presentación en Canva.:@0.755005:0.529881:0.903463:0.529881:0.903463:0.515887:0.755005:0.515887:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©Wikimedia Commons:@0.893746:0.247282:0.893746:0.177457:0.881835:0.177457:0.881835:0.247282:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En la actualidad, muchas :@0.754768:0.702502:0.922860:0.702502:0.922860:0.687603:0.754768:0.687603:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comunidades indígenas :@0.754768:0.717589:0.918959:0.717589:0.918959:0.702690:0.754768:0.702690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
continúan recreando sus :@0.754768:0.732677:0.923515:0.732677:0.923515:0.717778:0.754768:0.717778:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
prácticas educativas :@0.754768:0.747765:0.892875:0.747765:0.892875:0.732866:0.754768:0.732866:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ancestrales, que permiten :@0.754768:0.762852:0.930514:0.762852:0.930514:0.747953:0.754768:0.747953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conocer no solo sus :@0.754768:0.777940:0.891166:0.777940:0.891166:0.763041:0.754768:0.763041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aspectos sociopolíticos :@0.754768:0.793028:0.912792:0.793028:0.912792:0.778128:0.754768:0.778128:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y socioculturales, :@0.754768:0.808115:0.871715:0.808115:0.871715:0.793216:0.754768:0.793216:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sino también sus :@0.754768:0.823203:0.871164:0.823203:0.871164:0.808304:0.754768:0.808304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conocimientos de ciencia.:@0.754768:0.838290:0.928724:0.838290:0.928724:0.823391:0.754768:0.823391:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Averigua acerca de algún :@0.754768:0.856936:0.918203:0.856936:0.918203:0.842942:0.754768:0.842942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conocimiento científico de :@0.754768:0.872024:0.925120:0.872024:0.925120:0.858030:0.754768:0.858030:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una nacionalidad indígena.:@0.754768:0.887111:0.930484:0.887111:0.930484:0.873118:0.754768:0.873118:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cívica:@0.818848:0.670061:0.863699:0.670061:0.863699:0.653160:0.818848:0.653160:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000
maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000
®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684192:0.079553:0.268045:0.061505:0.268045:0.061505:0.684192:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000