# How do you find the solution to the quadratic equation  (x - 5)^2 + 2(x - 5) - 35 = 0 ?

May 1, 2015

Easier if you let $p = x - 5$,
solve the equation for "p" ,
then substitute back to get the values for $x$

${\left(x - 5\right)}^{2} + 2 \left(x - 5\right) - 35 = 0$

${p}^{2} + 2 p - 35 = 0$

$\left(p + 7\right) \left(p - 5\right) = 0$

If $p + 7 = 0$
then
$x - 5 + 7 = 0$
$x = - 2$

If $p - 5 = 0$
then
$x - 5 - 5 = 0$
$x = 10$

The solutions for the given quadratic equation are
$x = - 2 \text{ and } x = 10$