The problem is to solve the equation $x^2 = -9$ for $x$.

1. Problem Description

The problem is to solve the equation $x^2 = -9$ for $x$.

2. Solution Steps

We are given the equation $x^2 = -9$.

To find $x$, we take the square root of both sides of the equation.

$\sqrt{x^2} = \sqrt{-9}$

$x = \pm \sqrt{-9}$

Since $\sqrt{-1} = i$, we can rewrite $\sqrt{-9}$ as $\sqrt{9} \cdot \sqrt{-1}$.

$x = \pm \sqrt{9} \cdot \sqrt{-1}$

$x = \pm 3i$

Therefore, the solutions are $x = 3i$ and $x = -3i$.

3. Final Answer

$x = \pm 3i$