Answer
$$p=\frac{\sqrt{101}-9}{10},\:p=\frac{-\sqrt{101}-9}{10}$$
Work Step by Step
Completing the square to solve the equation, we find:
$$ 5\left(p^2+\frac{9p}{5}-\frac{1}{5}+\left(\frac{9}{10}\right)^2-\left(\frac{9}{10}\right)^2\right) \\ 5\left(\left(p+\frac{9}{10}\right)^2-\frac{1}{5}-\left(\frac{9}{10}\right)^2\right) \\ 5\left(p+\frac{9}{10}\right)^2-\frac{101}{20} \\ \left(p+\frac{9}{10}\right)^2=\frac{101}{100} \\ p=\frac{\sqrt{101}-9}{10},\:p=\frac{-\sqrt{101}-9}{10}$$
