We have , $x^2+x+\frac{1}{\sqrt{2}}$ = 0 Comparing the given equation with the general form $ax^2$ + bx + c = 0, we get a = 1 , b = 1 , c = $\frac{1}{\sqrt{2}}$ ∴ x = $\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ = $\frac{-1\pm\sqrt{(1)^2-4\times1\times\frac{1}{\sqrt{2}}}}{2.1}$ = $\frac{-1\pm\sqrt{1-2\sqrt{2}}}{2}$ = $\frac{-1\pm\sqrt{-(2\sqrt{2})-1)}}{2}$ = $\frac{-1\pm i\sqrt{2\sqrt{2}-1}}{2}$ ∴ The roots of the given equation are $\frac{-1+i\sqrt{2\sqrt{2}-1}}{2}$ and $\frac{-1-i\sqrt{2\sqrt{2}-1}}{2}$