Answer
$x=\left\{ -1-\sqrt{7},-1+\sqrt{7} \right\}$
Work Step by Step
The left side of the given equation, $
x^2+2x+1=7
,$ is a perfect square trinomial whose factored form is
\begin{array}{l}\require{cancel}
(x+1)^2=7
.\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+1=\pm\sqrt{7}
\\\\
x=-1\pm\sqrt{7}
.\end{array}
Hence, $
x=\left\{ -1-\sqrt{7},-1+\sqrt{7} \right\}
.$
