Answer
$x=-4i\text{ OR }x=4i$
Work Step by Step
Using the properties of equality, the given equation, $
x^2+16=0
,$ is equivalent to
\begin{align*}
x^2=-16
.\end{align*}
Taking the square root of both sides, the equation above is equivalent to
\begin{align*}
x&=\sqrt{-16}
\\
x&=\sqrt{-1}\cdot\sqrt{16}
\\
x&=\sqrt{-1}\cdot\pm4
\\
x&=i\cdot\pm4
&\text{ (use $i=\sqrt{-1}$)}
\\
x&=\pm4i
.\end{align*}
Hence, the solution to the given equation is $
x=-4i\text{ OR }x=4i
$.
