Answer
See below
Work Step by Step
$ x^{2}+6x=7\qquad$..add $9$ to both sides to complete the square ($\displaystyle \frac{1}{2}(6)=3$, and $3^{2}=9$.)
$ x^{2}+6x+9=7+9\qquad$...simplify by applying
the Perfect square formula ($(x+a)^{2}=x^{2}+2ax+a^{2}$) and adding like terms.
$(x+3)^{2}=16$
According to the general principle of square roots:
For any real number $k$ and any algebraic expression $x$ :
$\text{If }x^{2}=k,\text{ then }x=\sqrt{k}\text{ or }x=-\sqrt{k}$.
$ x+3=\pm\sqrt{16}\qquad$...add $-3$ to each side.
$ x+3-3=\pm\sqrt{16}-3\qquad$...simplify.
$x=-3\pm 4$
$x=-3+4$ or $x=-3-4$
$x=1$ or $x=-7$