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The given equation is:

\[
x^2 + 4 = 0
\]

We want to solve this equation for \( x \).

First, subtract 4 from both sides to isolate the \( x^2 \) term:

\[
x^2 = -4
\]

Next, take the square root of both sides:

\[
x = \pm \sqrt{-4}
\]

Since we have the square root of a negative number, the solutions are imaginary. Specifically:

\[
x = \pm 2i
\]

Where \( i \) is the imaginary unit, which represents \( \sqrt{-1} \).

Therefore, the correct answer to the question is **imaginary**.

Do you want more details on this, or have any questions?

Here are 5 related questions to explore:
1. How do you solve quadratic equations in general?
2. What are real and imaginary numbers?
3. When do quadratic equations have real solutions versus imaginary solutions?
4. Can you explain complex numbers and how they relate to imaginary numbers?
5. How does the quadratic formula apply to equations with complex solutions?

**Tip:** When solving quadratic equations, the discriminant \( b^2 - 4ac \) helps determine whether solutions are real or imaginary.

What are the types of solutions for x in the equation x^2 + 4 = 0?

Learn how to solve the quadratic equation x^2 + 4 = 0 and discover why the solutions are imaginary. This problem involves algebraic concepts, including quadratic equations and the square root of negative numbers. Suitable for students in Grades 9-10.

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