The equation \( x^2 = -9 \) does not have any real solutions because the square of any real number is non-negative, meaning \( x^2 \) cannot equal a negative number.
However, if we consider complex numbers, we can find solutions. Specifically, the solutions in the complex number system would be \( x = 3i \) and \( x = -3i \).
So, to summarize:
- The equation has 0 real solutions.
- The equation has 2 complex solutions.
If the question is purely about solutions in the real number system, the answer is 0.