Answer
The solutions are $x=-8$, $x=6$, $x=-6$ and $x=4$
Work Step by Step
$|x^{2}+2x-36|=12$
Solving an absolute value equation is equivalent to solving two separate equations. In this case, the equations are $x^{2}+2x-36=12$ and $x^{2}+2x-36=-12$
Solve the first equation:
$x^{2}+2x-36=12$
Take $12$ to the left side and simplify:
$x^{2}+2x-36-12=0$
$x^{2}+2x-48=0$
Solve by factoring:
$(x+8)(x-6)=0$
Set both factors equal to $0$ and solve each individual equation for $x$:
$x+8=0$
$x=-8$
$x-6=0$
$x=6$
Solve the second equation:
$x^{2}+2x-36=-12$
Take $12$ to the left side and simplify:
$x^{2}+2x-36+12=0$
$x^{2}+2x-24=0$
Solve by factoring:
$(x+6)(x-4)=0$
Set both factors equal to $0$ and solve each individual equation for $x$:
$x+6=0$
$x=-6$
$x-4=0$
$x=4$
The solutions are $x=-8$, $x=6$, $x=-6$ and $x=4$
