Answer
$x=\left\{ 3-\sqrt{15},3+\sqrt{15} \right\}$
Work Step by Step
Taking the square root of both sides (the Square Root Property), the solutions to the given equation, $
(x-3)^2=15
,$ are
\begin{array}{l}\require{cancel}
x-3=\pm\sqrt{15}
\\\\
x=3\pm\sqrt{15}
.\end{array}
Hence, $
x=\left\{ 3-\sqrt{15},3+\sqrt{15} \right\}
.$