Answer
$x=6$ and $x=-10$.
Work Step by Step
$(x+2)^{2}=64$
Taking square root on both sides, we get
$x+2=\pm\sqrt {64}$
$\implies x+2=\pm 8$
Subtracting $2$ from both sides, we obtain
$x=-2\pm 8$
So, the solutions are $x=-2+8=6$ and $x=-2-8=-10$.