Question

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

Answer 1

The given equation is

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

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

The roots of the quadratic equation $A{x}^2+Bx+C=0$ are

$x=\frac{-B\pm \sqrt{B^2-4AC}}{2A}$

for the given equation, $B^2-4AC$ is

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

$=1-8=-7$

So the roots are

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

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