The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -3.2679\\[1 em]x_2 &= -6.7321 \end{aligned} $$The solutions of $ x^2+10x+22 = 0 $ are: $ x = -5-\sqrt{ 3 } ~ \text{and} ~ x = -5+\sqrt{ 3 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.