Solving Quadratic Equations Using Common Factors Practice

To solve the quadratic equation \(x^2 - 13x + 42 = 0\) by grouping, we need to split the middle term \(-13x\) into two terms that add up to \(-13\) and multiply to \(42\).

We need two numbers that:

1. Multiply to \(42\) (the constant term).
2. Add up to \(-13\) (the coefficient of the middle term, which is negative).

After checking the pairs of factors of \(42\):

- \(1\) and \(42\) (sum is \(43\))
- \(2\) and \(21\) (sum is \(23\))
- \(3\) and \(14\) (sum is \(17\))
- \(6\) and \(7\) (sum is \(13\))

The pair that works here is \(-6\) and \(-7\):

- \(-6 \times -7 = 42\)
- \(-6 + (-7) = -13\)

Thus, the two numbers needed to complete the step are \(-6\) and \(-7\).

So, you should enter:

**-7, -6** (enter the lesser value first).