To solve the quadratic equation \(x^2 - 6x + 8 = 0\), we can use factoring, completing the square, or the quadratic formula. Let's solve this by factoring:

### Step 1: Set up the equation
We have the equation:

\[
x^2 - 6x + 8 = 0
\]

### Step 2: Find factors of 8 that add up to -6
We need two numbers that multiply to 8 and add up to -6. The numbers are -2 and -4, because:

\[
(-2) \times (-4) = 8 \quad \text{and} \quad (-2) + (-4) = -6
\]

### Step 3: Factor the quadratic
We can now write the equation as:

\[
(x - 2)(x - 4) = 0
\]

### Step 4: Solve for \(x\)
Now set each factor equal to zero:

\[
x - 2 = 0 \quad \text{or} \quad x - 4 = 0
\]

Solving these gives:

\[
x = 2 \quad \text{or} \quad x = 4
\]

### Final Answer:
The solutions are \(x = 2\) and \(x = 4\).

Would you like more details on this process or have any questions?

Here are 5 related questions to deepen your understanding:
1. How can you verify that \(x = 2\) and \(x = 4\) are correct solutions?
2. What is the general form of a quadratic equation?
3. How would you solve \(x^2 - 6x + 9 = 0\)?
4. How does the quadratic formula apply to this equation?
5. How can completing the square solve \(x^2 - 6x + 8 = 0\)?

**Tip:** Always check your solutions by plugging them back into the original equation.

Learn how to solve the quadratic equation X^2 - 6x + 8 by factoring. This step-by-step solution walks through finding the factors of the quadratic and applying the zero product property. Suitable for students in Grades 8-10, covering core algebra concepts and techniques.

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