The equation presented is:

$x^2 = -25$

To solve this equation:

1. Isolate the squared term: The equation is already in the form $x^2 = -25$, so we can now proceed to the next step.
2. Take the square root of both sides: To solve for $x$, take the square root of both sides of the equation.

$x = \pm \sqrt{-25}$

However, the square root of a negative number introduces an imaginary number. So, we express the square root of $-25$ as:

$x = \pm 5i$

where $i$ is the imaginary unit, defined by $i = \sqrt{-1}$.

Thus, the solutions are:

$x = 5i \quad \text{or} \quad x = -5i$

Let me know if you need any further clarifications!

Follow-up Questions:

1. What is the definition of an imaginary number?
2. How can we solve equations with higher powers involving imaginary numbers?
3. What are some real-world applications of imaginary numbers?
4. How do square roots of negative numbers differ from square roots of positive numbers?
5. What other types of equations result in complex number solutions?

Tip: When solving equations involving imaginary numbers, always look for negative values inside the square root and apply the imaginary unit $i$.