The equation is:

\[
x^2 + 25 = 0
\]

To solve for \( x \), we can isolate \( x^2 \) by moving \( 25 \) to the other side of the equation:

\[
x^2 = -25
\]

To solve for \( x \), we take the square root of both sides. However, the square root of a negative number requires complex numbers:

\[
x = \pm \sqrt{-25}
\]

Using the imaginary unit \( i \) where \( i = \sqrt{-1} \), we get:

\[
x = \pm 5i
\]

### Solution
\[
x = 5i \quad \text{or} \quad x = -5i
\]

Would you like a further explanation or have any questions?

Here are 5 related questions for further practice:
1. Solve \( x^2 + 36 = 0 \).
2. Solve \( x^2 - 16 = 0 \).
3. Find the roots of \( x^2 + 9 = 0 \).
4. Solve \( x^2 + 1 = 0 \).
5. Solve \( x^2 - 25 = 0 \).

**Tip:** When taking the square root of a negative number, use the imaginary unit \( i \).

Learn how to solve the quadratic equation x^2 + 25 = 0 by introducing complex numbers. This solution explains how to handle negative square roots using the imaginary unit i and covers key concepts in algebra and complex number theory. Suitable for students in Grades 10-12.

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