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 x^2−13x+42=0 , which two numbers would be needed to complete this step? Enter the lesser value first.(1 point) x^2−13x+42=0 x^2+() x+() x+42=0

Answer 1

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

The two numbers that fit these criteria are -6 and -7, because:

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

Thus, when we rewrite the equation, we can express it as:

\[ x^2 - 6x - 7x + 42 = 0 \]

So we can fill in the blanks as follows:

\( x^2 + (-6)x + (-7)x + 42 = 0 \)

Therefore, the answer is:

-6 and -7 (with -6 being the lesser value).