Which of these potential solutions make the equation x^2 + 9 = 0 true?

1 answer

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.