Question

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

x2+
x+
x+42=0

Answer 1

To find two numbers that can be used to rewrite the middle term \(-13x\) in the equation \(x^2 - 13x + 42 = 0\), we need to look for two numbers that multiply to \(42\) (the constant term) and add up to \(-13\) (the coefficient of the middle term).

Let's consider the pairs of factors of \(42\):

- \(1 \cdot 42\)
- \(2 \cdot 21\)
- \(3 \cdot 14\)
- \(6 \cdot 7\)

Now, we need the pair that adds to \(-13\). To achieve that, we will also consider using negative values:

1. \(-1 + (-42) = -43\)
2. \(-2 + (-21) = -23\)
3. \(-3 + (-14) = -17\)
4. \(-6 + (-7) = -13\)

The pair \(-6\) and \(-7\) multiplies to \(42\) and adds to \(-13\).

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

So, the answer is:
-6, -7