#### Answer

$x_{1}=\sqrt{7}i$ and $x_{2}=-\sqrt{7}i$

#### Work Step by Step

Given $x^2+7=0$
$a=1,\ b=0,\ c=7$
Using the quadratic formula: $\dfrac{-b\pm \sqrt{b^2-4ac}}{2a} , $ we have:
$\dfrac{-0\pm \sqrt{0^2-4\times 1\times 7}}{2\times 1} = \dfrac{\pm \sqrt{-28}}{2} = \pm \dfrac{\sqrt{28}i}{2} = \pm \dfrac{2\sqrt{7}i}{2} = \pm \sqrt{7}i$
Therefore, the solutions are: $x_{1}=\sqrt{7}i$ and $x_{2}=-\sqrt{7}i$