The equation \( x^2 = -9 \) does not have any real solutions because the square of a real number cannot be negative. However, if you consider complex numbers, the solutions would be \( x = 3i \) and \( x = -3i \), where \( i \) is the imaginary unit.
Since the question asks for the number of solutions, the equation \( x^2 = -9 \) has 2 solutions in the realm of complex numbers.
So the answer is: 2 solution(s).