Question:
$x^{2}+2=0$
Solution:
This equation is a quadratic equation
Solution of a general quadratic equation $a x^{2}+b x+c=0$ is given by:
$x=\frac{-b \pm \sqrt{\left(b^{2}-4 a c\right)}}{2 a}$
Given:
$\Rightarrow \mathrm{x}^{2}+2=0$
$\Rightarrow \mathrm{x}^{2}=-2$
$\Rightarrow \mathrm{x}=\pm \sqrt{(-2)}$
But we know that $\sqrt{(-1)}=\mathrm{i}$
$\Rightarrow x=\pm \sqrt{2} i$
Ans: $x=\pm \sqrt{2} i$