Answer
$x=\left\{
-3i,3i
\right\}
$
Work Step by Step
Using $ax^2+bx+c=0,$ the given equation,
\begin{align*}
x^2+9=0
,\end{align*} has $a=
1
,$ $b=
0
,$ and $c=
9
.$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}
x&=\dfrac{-0\pm\sqrt{0^2-4(1)(9)}}{2(1)}
\\\\
x&=\dfrac{\pm\sqrt{-36}}{2}
\\\\
x&=\dfrac{\pm\sqrt{-1}\cdot\sqrt{36}}{2}
\\\\
x&=\dfrac{\pm\sqrt{-1}\cdot6}{2}
\\\\
x&=\dfrac{\pm i\cdot6}{2}
\\\\
x&=\pm\dfrac{6i}{2}
\\\\
x&=\pm3i
.\end{align*}
The solutions are $
x=\left\{
-3i,3i
\right\}
.$
