Question

Slolucion de la ecuacion cuadratica (x-5)²-(x-6)²=(2x-3)²-118

Answer 1

$\left(x-5\right)^2-\left(x-6\right)^2=\left(2x-3\right)^2-118$

$\mathrm{Aplicar}:\quad \left(a-b\right)^2=a^2-2ab+b^2$

$x^2-10x+25-(x^2-12x+36)=4x^2-12x-109-118$

$\mathrm{Simplificar:}$

$2x-11=4x^2-12x-109$

$4x^2-12x-98=2x$

$4x^2-12x-98=2x$

$4x^2-14x-98=0$

$\mathrm{Factorizar}:$

$(x-7)(2x+7)=0$

$x=7,\:x=-\frac{7}{2}$