The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 18.0998\\[1 em]x_2 &= -22.0998 \end{aligned} $$The solutions of $ x^2+4x-400 = 0 $ are: $ x = -2-2 \sqrt{ 101 } ~ \text{and} ~ x = -2+2 \sqrt{ 101 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.