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=0x2+x+x+42=0

Answer 1

To solve the quadratic equation \( x^2 - 13x + 42 = 0 \) by factoring through grouping, we need to find two numbers that multiply to the constant term (which is 42) and add up to the coefficient of the linear term (which is -13).

1. Identify the product: \( 42 \)
2. Identify the sum: \( -13 \)

We need to find two numbers that satisfy these conditions.

The pairs of factors of \( 42 \) are:

• \( 1 \) and \( 42 \)
• \( 2 \) and \( 21 \)
• \( 3 \) and \( 14 \)
• \( 6 \) and \( 7 \)

Out of these pairs, we need to identify which pair sums to \( -13 \).

Considering the negatives:

• \( -6 \) and \( -7 \) multiply to \( 42 \) and add to \( -13 \).

Thus, the two numbers we are looking for are \( -6 \) and \( -7 \).

So the answer, entering the lesser value first, is: \[ -7, -6 \]