The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.127\\[1 em]x_2 &= -8.873 \end{aligned} $$The solutions of $ x^2+10x+10 = 0 $ are: $ x = -5-\sqrt{ 15 } ~ \text{and} ~ x = -5+\sqrt{ 15 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.