The equation given is:

\[
x^2 - 10 + 25 = 0
\]

Let's simplify it step by step:

1. Combine constants \(-10\) and \(25\):

\[
x^2 + 15 = 0
\]

2. To solve for \(x\), subtract \(15\) from both sides:

\[
x^2 = -15
\]

3. Since \(x^2 = -15\), there is no real solution because the square of a real number cannot be negative. However, we can express the solution using imaginary numbers.

4. Take the square root of both sides:

\[
x = \pm \sqrt{-15} = \pm \sqrt{15}i
\]

Thus, the solutions are:

\[
x = \pm \sqrt{15}i
\]

Would you like more details or have any questions?

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Here are 5 related questions:
1. What is an imaginary number?
2. How do you simplify expressions with imaginary numbers?
3. What are complex numbers, and how do they relate to imaginary numbers?
4. How can we solve quadratic equations with imaginary solutions?
5. What is the geometric interpretation of imaginary numbers?

**Tip:** When encountering negative square roots, use imaginary numbers to handle them.

Explore how to solve the quadratic equation x² - 10 + 25 = 0 and understand the use of imaginary numbers in algebra. This problem demonstrates key algebraic concepts, including combining constants and solving equations with negative square roots. Suitable for students in Grades 9-10.

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