Answer
$\left\{ \dfrac{-\sqrt{2}- i\sqrt{2}}{2},\dfrac{-\sqrt{2}+ i\sqrt{2}}{2} \right\}$
Work Step by Step
Using $\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ (or the Quadratic Formula), the solutions of the given quadratic equation, $
x^2+\sqrt{2}x+1=0
,$ are
\begin{array}{l}\require{cancel}
\dfrac{-(\sqrt{2})\pm\sqrt{(\sqrt{2})^2-4(1)(1)}}{2(1)}
\\\\=
\dfrac{-\sqrt{2}\pm\sqrt{2-4}}{2}
\\\\=
\dfrac{-\sqrt{2}\pm\sqrt{-2}}{2}
\\\\=
\dfrac{-\sqrt{2}\pm\sqrt{-1}\sqrt{2}}{2}
\\\\=
\dfrac{-\sqrt{2}\pm i\sqrt{2}}{2}
.\end{array}
Hence, the solutions are $
\left\{ \dfrac{-\sqrt{2}- i\sqrt{2}}{2},\dfrac{-\sqrt{2}+ i\sqrt{2}}{2} \right\}
.$
