#### Answer

$x=\{ -1,7 \}
$

#### Work Step by Step

Taking the square root of both sides (the Square Root Property), the solutions to the given equation, $
(x-3)^2=16
,$ are
\begin{array}{l}\require{cancel}
(x-3)=\pm\sqrt{16}
\\\\
x-3=\pm\sqrt{(4)^2}
\\\\
x-3=\pm4
\\\\
x=3\pm4
.\end{array}
Hence, $
x=\{ -1,7 \}
.$