To solve the equation \( x^2 + 4 = 0 \), we can isolate \( x^2 \):
\[ x^2 = -4 \]
Next, we take the square root of both sides:
\[ x = \pm \sqrt{-4} \]
Since we are taking the square root of a negative number, we introduce the imaginary unit \( i \):
\[ x = \pm 2i \]
The solutions \( 2i \) and \( -2i \) are both imaginary numbers. Therefore, the types of solutions for \( x \) in this equation are:
Imaginary.