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To solve the quadratic equation \(x^2 - 6x + 5 = 0\) by completing the square, follow these steps:

### Step 1: Move the constant to the other side of the equation
Start by rewriting the equation:

\[
x^2 - 6x = -5
\]

### Step 2: Complete the square
To complete the square, take half of the coefficient of \(x\), square it, and add it to both sides of the equation. The coefficient of \(x\) is \(-6\), so:

\[
\left(\frac{-6}{2}\right)^2 = 9
\]

Add 9 to both sides of the equation:

\[
x^2 - 6x + 9 = -5 + 9
\]

\[
(x - 3)^2 = 4
\]

### Step 3: Solve for \(x\)
Now take the square root of both sides:

\[
x - 3 = \pm 2
\]

So,

\[
x = 3 \pm 2
\]

This gives two solutions:

\[
x = 3 + 2 = 5 \quad \text{or} \quad x = 3 - 2 = 1
\]

### Final Answer:
The solutions are \(x = 5\) and \(x = 1\). Thus, the correct option is:
\[
\boxed{x = 5, 1}
\]

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How does completing the square compare to using the quadratic formula?
2. Can you apply the method of completing the square to other forms of quadratics, such as those with a leading coefficient other than 1?
3. How would the solution change if the quadratic term had a different sign (e.g., \( -x^2 \))?
4. What is the geometric interpretation of completing the square on a quadratic function?
5. How can completing the square help in deriving the quadratic formula?

**Tip:** When completing the square, always ensure that the coefficient of \(x^2\) is 1 before proceeding. If it isn't, divide the entire equation by that coefficient first!

Solve x^2 - 6x + 5 = 0 by completing the square.

Learn how to solve the quadratic equation x^2 - 6x + 5 = 0 using the method of completing the square. This problem covers algebraic techniques suitable for students in Grades 8-10, providing a step-by-step guide to find the solutions x = 5 and x = 1.

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