#### Answer

$x=\left\{ -6,5 \right\}$

#### Work Step by Step

The factored form of the given expression, $
x^2+(x+1)^2=61
$, is
\begin{array}{l}
x^2+x^2+2x+1-61=0
\\\\
2x^2+2x-60=0
\\\\
x^2+x-30=0
\\\\
(x+6)(x-5)=0
.\end{array}
Equating each factor to zero, then
\begin{array}{l}
x+6=0
\\
x=0-6
\\
x=-6
,\text{ OR}\\\\
x-5=0
\\
x=0+5
\\
x=5
\end{array}
Hence, $
x=\left\{ -6,5 \right\}
$.