#### Answer

$x=4$ and $x=-10$

#### Work Step by Step

$x^{2}+6x-40=0$
Add $40$ to both sides of the equation to obtain
$x^{2}+6x=40$
Add $(\frac{b}{2})^{2}=(\frac{6}{2})^{2}=3^{2}$ to both sides to complete the square.
$x^{2}+6x+3^{2}=40+3^{2}$
$\implies (x+3)^{2}=49$
Taking square root on both sides, we have
$x+3=\pm7$
$\implies x=-3\pm7$
The solutions of the given equation are $x=-3+7=4$ and $x=-3-7=-10$