Question

Solve :
$x^2+\frac{x}{\sqrt{2}}+1=0$

Answer 1

$x^2+\frac{x}{\sqrt{2}}+1=0$

$\Rightarrow \sqrt{2}{x}^2+x+\sqrt{2}=0$

$x=\frac{-\left(1\right)\pm \sqrt{(1{)}^2-4(\sqrt{2}\left)\right(\sqrt{2})}}{2\left(\sqrt{2}\right)}$

$=\frac{-1\pm \sqrt{1-8}}{2\sqrt{2}}$

$=\frac{-1\pm \sqrt{7}i}{2\sqrt{2}}$.