To determine if any potential solutions make the equation \( x^2 + 9 = 0 \) true, we need to solve for \( x \).
Starting with the equation:
\[ x^2 + 9 = 0 \]
Subtracting 9 from both sides gives:
\[ x^2 = -9 \]
To solve for \( x \), we take the square root of both sides:
\[ x = \pm \sqrt{-9} \]
This simplifies to:
\[ x = \pm 3i \]
where \( i \) is the imaginary unit, representing \( \sqrt{-1} \).
Therefore, the solutions to the equation \( x^2 + 9 = 0 \) are:
\[ x = 3i \quad \text{and} \quad x = -3i \]
These are the values of \( x \) that make the equation true. If any potential solutions include \( 3i \) or \( -3i \), then they make the equation true.