Question

One of the steps needed to solve a quadratic equation by grouping is to split the middle term as a sum of two terms. Given the equation x2−13x+42=0
, which two numbers would be needed to complete this step? Enter the lesser value first.(1 point)
x2−13x+42=0

Answer 1

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

We are looking for two numbers that:
1. Multiply to \( 42 \) (the constant term)
2. Add up to \( -13 \) (the coefficient of the middle term)

The pairs of factors of \( 42 \) are:
- \( 1 \) and \( 42 \)
- \( 2 \) and \( 21 \)
- \( 3 \) and \( 14 \)
- \( 6 \) and \( 7 \)

Now, we also need to consider their negative counterparts since we need to sum to a negative number (-13). The relevant pairs for our purpose would be:
- \( -6 \) and \( -7 \) (since \( -6 + -7 = -13 \) and \( -6 \times -7 = 42 \))

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

To summarize, the answer is:
\[
-7, -6
\]