\begin{align*}
  x^2+2x+2 &> 50 \\
  (x+1)^2 + 1 &> 50 \qquad \text{(første kv. setning)} \\
  (x+1)^2 &> 49 \\
  x+1 &> \pm\sqrt{49} \\
\end{align*}

Vi deler opp likningen

\begin{align*}
  -\sqrt{49} &< x+1 &&\vee& x+1 &< \sqrt{49} \\
  -7 &< x+1 &&\vee& x+1 &< 7 \\
  -8 &< x &&\vee& x &< 6 \\
\end{align*}
\[x \in \left(-8,6\right)\]