Answer
$x=\left\{ -20i,20i \right\}$
Work Step by Step
Taking the square root of both sides, the solutions to the given equation, $
x^2=-400
,$ are
\begin{array}{l}\require{cancel}
x=\pm\sqrt{-400}
\\\\
x=\pm\sqrt{-1}\cdot\sqrt{400}
\\\\
x=\pm i\cdot\sqrt{(20)^2}
\\\\
x=\pm i\cdot20
\\\\
x=\pm20i
.\end{array}
Hence, the solution is $
x=\left\{ -20i,20i \right\}
.$
