#### Answer

$\left\{-4, 4\right\}$

#### Work Step by Step

RECALL:
If $x^2=a$, then taking the square root of both sides gives $x = \pm \sqrt{a}$.
Take the square root of both sides of the given equation to obtain:
$\sqrt{x^2}=\pm \sqrt{16}
\\x =\pm \sqrt{4^2}
\\x=\pm 4$
Thus, the solution set is $\left\{-4, 4\right\}$.