Final answer:
The equation x² = -64 has no real solutions, but it has 2 complex solutions, which are 8i and -8i.
Step-by-step explanation:
The equation in question is x² = -64. In the realm of real numbers, no real number squared can give a negative result, as the square of a real number is always nonnegative. Therefore, the equation x² = -64 has no real solutions. However, if we consider complex numbers, there are two solutions to this equation, which are x = 8i and x = -8i, where i is the imaginary unit, equal to the square root of -1. Thus, there are 2 complex solutions to the equation.