Answer
$x=\left\{ -4,4 \right\}$
Work Step by Step
Taking the square root of both sides, the solutions to the given equation, $
x^2=16
,$ are
\begin{array}{l}\require{cancel}
x=\pm\sqrt{16}
\\\\
x=\pm\sqrt{(4)^2}
\\\\
x=\pm4
.\end{array}
Hence, the solution is $
x=\left\{ -4,4 \right\}
.$