Answer
$y=\left\{ -5,3 \right\}$
Work Step by Step
The factored form of the given expression, $
y^2+(y+2)^2=34
$, is
\begin{array}{l}
y^2+(y+2)^2=34
\\\\
y^2+y^2+4y+4-34=0
\\\\
2y^2+4y-30=0
\\\\
y^2+2y-15=0
\\\\
(y+5)(y-3)=0
.\end{array}
Equating each factor to zero, then
\begin{array}{l}
y+5=0
\\
y=0-5
\\
y=-5
,\text{ OR}\\\\
y-3=0
\\
y=0+3
\\
y=3
\end{array}
Hence, $
y=\left\{ -5,3 \right\}
$.
