Answer
$\left\{-2i\sqrt{3},2i\sqrt{3}\right\}$
Work Step by Step
Taking the square root of both sides (Square Root Property), the given equation, $
x^2=-12
,$ is equivalent to
\begin{align*}
x&=\pm\sqrt{-12}
.\end{align*}
Using the properties of radicals, the equation above is equivalent to
\begin{align*}
x&=\pm\sqrt{12\cdot(-1)}
\\&=
\pm\sqrt{12}\cdot\sqrt{-1}
\\&=
\pm\sqrt{4\cdot3}\cdot\sqrt{-1}
\\&=
\pm2\sqrt{3}\cdot\sqrt{-1}
\\&=
\pm2\sqrt{3}\cdot i
&(\text{use }i=\sqrt{-1})
\\&=
\pm2i\sqrt{3}
.\end{align*}
Hence, the solution set of the equation $
x^2=-12
$ is $\left\{-2i\sqrt{3},2i\sqrt{3}\right\}$.
