Question

One of the steps needed to solve a quadratic equation by grouping just to split the middle term as the sum of two terms given the equation x squared - 13x + 42 = 0 which two numbers would be needed to complete this step enter the lesser value first
X squared - 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 such that their sum equals \(-13\) and their product equals the constant term \(42\).

Let's denote the two numbers we need as \(a\) and \(b\). The conditions we need are:

1. \(a + b = -13\)
2. \(a \cdot b = 42\)

To find \(a\) and \(b\), we can look for two numbers that multiply to \(42\) and add up to \(-13\).

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

We can take the negatives of these pairs because we are seeking a sum of \(-13\):
- \(-1\) and \(-42\) (sum is \(-43\))
- \(-2\) and \(-21\) (sum is \(-23\))
- \(-3\) and \(-14\) (sum is \(-17\))
- \(-6\) and \(-7\) (sum is \(-13\))

The correct pair \(a\) and \(b\) is \(-6\) and \(-7\).

Thus, the two numbers that need to be used to split the middle term are \(-6\) and \(-7\). Since you asked for the lesser value first:

**Answer: -7, -6**