Answer
The solutions are $-1-4\sqrt{2}$ and $-1+4\sqrt{2}$.
Work Step by Step
$ 7q^{2}+10q=2q^{2}+155\qquad$ ...add $-2q^{2}$ to each side
$ 5q^{2}+10q=155\qquad$ ...divide the entire expression with $5$.
$ q^{2}+2q=31\qquad$ ...square half the coefficient of $q$.
$(\displaystyle \frac{2}{2})^{2}=1^{2}=1\qquad$ ...complete the square by adding$ 1$ to each side of the expression
$ q^{2}+2q+1=31+1\qquad$ ...Write $q^{2}+2q+1$ as a binomial squared.
$(q+1)^{2}=32\qquad$ ...take square roots of each side.
$ q+1=\pm\sqrt{32}\qquad$ ...simplify $\sqrt{32}=\sqrt{4\cdot 4\cdot 2}=4\sqrt{2}$
$ q+1=\pm 4\sqrt{2}\qquad$ ...add $-1$ to each side.
$q=-1\pm 4\sqrt{2}$
