Answer
$y=\left\{ 7-3\sqrt{2},7+3\sqrt{2} \right\}$
Work Step by Step
The left side of the given equation, $
y^2-14y+49=18
,$ is a perfect square trinomial whose factored form is
\begin{array}{l}\require{cancel}
(y-7)^2=18
.\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}
y-7=\pm\sqrt{18}
\\\\
y-7=\pm\sqrt{9\cdot2}
\\\\
y-7=\pm\sqrt{(3)^2\cdot2}
\\\\
y-7=\pm3\sqrt{2}
\\\\
y=7\pm3\sqrt{2}
.\end{array}
Hence, $
y=\left\{ 7-3\sqrt{2},7+3\sqrt{2} \right\}
.$
