Question

Resolva a equação
x2+(x+1).(x+1)=25

Answer 1

$\sf x^2+(x+1)\cdot(x+1)=25\\x^2+x^2+x+x+1=25\\2x^2+2x+1=25\\2x^2+2x=25-1\\2x^2+2x=24\\2x^2+2x-24=0$

$\sf a = 2\\b = 2 \\c= -24\\\\2^2 - 4 \cdot 2 \cdot - 24\\4 - 8 \cdot - 24\\4 -- 192\\\Delta = 196 \ \ \sqrt{\Delta} = \sqrt{196} = 14.\\\\x_1 = \cfrac{-2 + 14}{4}\\\\\boxed{\sf x_1 = 3}\\\\x_2 = \cfrac{-2 - 14}{4}\\\\\boxed{\sf x_2 = -4}$