Solve the following equation.
(Simplify your answer. Express complex numbers in terms of . Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)
x^2 + 64 = 0
x^2 + 64 = 0
Let's subtract 64 from both sides of the equation:
x^2 = -64
To solve for x, we take the square root of both sides:
√(x^2) = √(-64)
x = ±√(-64)
Since we have a square root of a negative number, we can deal with it by using the imaginary unit i, where i^2 = -1.
x = ±√(64) * √(-1)
x = ±8i
Therefore, the solutions to the equation are x = 8i and x = -8i.