Answer
$x=\{ -2,2 \}$
Work Step by Step
Using the properties of equality, the given equation, $
4x^2=16
,$ is equivalent to
\begin{align*}
\dfrac{4x^2}{4}&=\dfrac{16}{4}
\\\\
x^2&=4
.\end{align*}
Getting the square root of both sides (Square Root Property), the equation above is equivalent to
\begin{align*}
x&=\pm\sqrt{4}
\\
x&=\pm2
.\end{align*}
Hence, the solutions are $
x=\{ -2,2 \}
$.