Solve for xxx if 2x2−8x+6=02x^2 - 8x + 6 = 02x2−8x+6=0.

To solve the quadratic equation \( 2x^2 - 8x + 6 = 0 \), follow these steps:

### Step 1: Simplify the equation
First, divide the entire equation by 2 to make the coefficient of \(x^2\) equal to 1:

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

\[
x^2 - 4x + 3 = 0
\]

### Step 2: Factor the quadratic
Now, we need to factor the quadratic equation \(x^2 - 4x + 3 = 0\). Find two numbers that multiply to give 3 and add to give -4. These numbers are -3 and -1. So, the factored form is:

\[
(x - 3)(x - 1) = 0
\]

### Step 3: Solve for \(x\)
Now, set each factor equal to zero:

\[
x - 3 = 0 \quad \text{or} \quad x - 1 = 0
\]

\[
x = 3 \quad \text{or} \quad x = 1
\]

### Final Answer:
The solutions are \(x = 3\) and \(x = 1\).

Would you like more details or further clarification?

Here are five questions to deepen your understanding:
1. What is the significance of factoring in solving quadratic equations?
2. How can you verify the solutions \(x = 3\) and \(x = 1\) are correct?
3. What other methods could be used to solve \(2x^2 - 8x + 6 = 0\)?
4. What happens if the quadratic doesn't factor easily—what method can be used?
5. Can quadratic equations have no real solutions?

**Tip:** When solving quadratics, always check for the greatest common factor (GCF) first. It can simplify the equation significantly!

Learn how to solve the quadratic equation 2x^2 - 8x + 6 = 0 using factoring and the Zero Product Property. This step-by-step guide simplifies the problem, ideal for students in Grades 8-10.

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