Answer
Answer: A
Work Step by Step
$ x^{2}+10x+8=-5\qquad$ ... write left side in the form $x^{2}+bx$ (add $-8$ to each side).
$ x^{2}+10x+8-8=-5-8\qquad$ ...simplify.
$ x^{2}+10x=-13\qquad$ ...square half the coefficient of $x$.
$(\displaystyle \frac{10}{2})^{2}=(5)^{2}=25\qquad$ ...add $5$ to each side of the expression
$ x^{2}+10x+25=-13+25\qquad$ ...simplify.
$ x^{2}+10x+25=12\qquad$ ... write left side as a binomial squared.
$(x+5)^{2}=12\qquad$ ...take square roots of each side.
$ x+5=\pm\sqrt{12}\qquad$ ...rewrite $\sqrt{12}$ as $\sqrt{4\cdot 3}$
$ x+5=\pm\sqrt{4\cdot 3.}\qquad$ ...evaluate $\sqrt{4}$.
$ x+5=\pm 2\sqrt{3}\qquad$ ...add $-5$ to each side.
$ x+5-5=\pm 2\sqrt{3}-5\qquad$ ...simplify.
$x=-5\pm 2\sqrt{3}$
