Answer
$x=\left\{ -3,9 \right\}$
Work Step by Step
The left side of the given equation, $
x^2-6x+9=36
,$ is a perfect square trinomial whose factored form is
\begin{array}{l}\require{cancel}
(x-3)^2=36
.\end{array}
Taking the square root of both sides (the Square Root Property), the solutions to the given equation are
\begin{array}{l}\require{cancel}
x-3=\pm\sqrt{36}
\\\\
x-3=\pm\sqrt{(6)^2}
\\\\
x-3=\pm6
\\\\
x=3\pm6
.\end{array}
Hence, $
x=\left\{ -3,9 \right\}
.$
