#### Answer

$\color{blue}{\left\{-20i, 20i\right\}}$

#### 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:
$\sqrt{x^2}=\pm \sqrt{-400}
\\x =\pm \sqrt{400(-1)}
\\x=\pm\sqrt{20^2(-1)}
\\x =\pm 20\sqrt{-1}$
Since $\sqrt{-1}=i$, then the solution is:
$x=\pm 20i$
Thus, the solution set is $\color{blue}{\left\{-20i, 20i\right\}}$.