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Let's solve the quadratic equation \( x^2 - 12x + 25 = 0 \) by completing the square, as your homework question asks.

### Steps:

1. **Move the constant term** to the right side:
   \[
   x^2 - 12x = -25
   \]

2. **Find the number to complete the square**:
   To complete the square, take half of the coefficient of \(x\) (which is \(-12\)), then square it:
   \[
   \left( \frac{-12}{2} \right)^2 = (-6)^2 = 36
   \]

3. **Add this value to both sides** of the equation:
   \[
   x^2 - 12x + 36 = -25 + 36
   \]
   Simplifying:
   \[
   (x - 6)^2 = 11
   \]

4. **Solve for \(x\)** by taking the square root of both sides:
   \[
   x - 6 = \pm \sqrt{11}
   \]

5. **Solve for \(x\)**:
   \[
   x = 6 \pm \sqrt{11}
   \]

Thus, the solutions are:
\[
x = 6 + \sqrt{11} \quad \text{or} \quad x = 6 - \sqrt{11}
\]

Now you can input this into the solution form as:

- Form: \( (x - 6)^2 = 11 \)
- Solution: \( x = 6 \pm \sqrt{11} \)

Would you like a more detailed explanation on any part of this process?

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Here are 5 related questions you might find useful:

1. How do you solve a quadratic equation using the quadratic formula?
2. What is the method of completing the square, and how does it compare to factoring?
3. What are the advantages of completing the square in solving quadratics?
4. How do we interpret solutions involving square roots like \( \sqrt{11} \)?
5. Can completing the square be used to derive the quadratic formula?

**Tip:** When completing the square, always ensure to balance the equation by adding the same value to both sides.

Solve the quadratic equation by completing the square: x^2 - 12x + 25 = 0

Learn how to solve the quadratic equation x^2 - 12x + 25 = 0 by completing the square. This method involves moving the constant term and adding a value to both sides to form a perfect square trinomial. Ideal for students in Grades 8-10.

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