Answer
$$s=\frac{3\sqrt{3}-5}{2},\:s=\frac{-3\sqrt{3}-5}{2}$$
Work Step by Step
Completing the square to solve the equation, we find:
$$ 2\left(s^2+5s-\frac{1}{2}+\left(\frac{5}{2}\right)^2-\left(\frac{5}{2}\right)^2\right) \\ 2\left(\left(s+\frac{5}{2}\right)^2-\frac{1}{2}-\left(\frac{5}{2}\right)^2\right) \\ 2\left(s+\frac{5}{2}\right)^2-\frac{27}{2} \\ \left(s+\frac{5}{2}\right)^2=\frac{27}{4} \\ s=\frac{3\sqrt{3}-5}{2},\:s=\frac{-3\sqrt{3}-5}{2}$$
