To solve the equation \( x^2 + 9 = 0 \), we can start by isolating \( x^2 \):
\[ x^2 = -9 \]
Next, we take the square root of both sides:
\[ x = \pm \sqrt{-9} \]
Since the square root of a negative number involves imaginary numbers, we can express this as:
\[ x = \pm 3i \]
Thus, the solutions to the equation \( x^2 + 9 = 0 \) are:
\[ x = 3i \quad \text{and} \quad x = -3i \]
These are the values that make the equation true.