I apologize for the mistake in step 5. The numbers \(-7\) and \(-6\) mentioned were incorrect and irrelevant to the factorization process.

Let's correct this.

### Correct Step 5: Factorizing the quadratic equation.

We have the quadratic equation:

\[
2x^2 - 13x + 14 = 0
\]

To factor this correctly, we need to find two numbers that multiply to the product of the coefficient of \(x^2\) (which is \(2\)) and the constant term (which is \(14\)), and add up to the coefficient of \(x\) (which is \(-13\)).

The product is:

\[
2 \times 14 = 28
\]

We need two numbers that multiply to \(28\) and add to \(-13\). These numbers are \(-7\) and \(-6\).

However, we made a mistake here before, let's re-check it:
   
1. Split the middle term correctly: 
\[
-7x - 6x \quad \text{instead of -7 and -6}
\]

### Let's correct this:

So we rewrite the quadratic as:
\[
2

Discover how to correct mistakes in quadratic equation factorization step-by-step. This problem covers the concept of factoring quadratic equations, with a detailed explanation on how to find correct factors. Suitable for high school students and those preparing for standardized tests.

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