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