Answer
$x=\left\{ -4,10 \right\}$
Work Step by Step
The left side of the given equation, $
x^2-6x+9=49
,$ is a perfect square trinomial whose factored form is
\begin{array}{l}\require{cancel}
(x-3)^2=49
.\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{49}
\\\\
x-3=\pm\sqrt{(7)^2}
\\\\
x-3=\pm7
\\\\
x=3\pm7
.\end{array}
Hence, $
x=\left\{ -4,10 \right\}
.$