Question

write two numbers that multiply to the value on top and add to the value on bottom.
-40
×
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6
answer attempt 1 out of 2
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Explanation:

Step1: Define variables and equations

Let the two numbers be \( x \) and \( y \). We have two equations:
\( xy=-40 \) (product is -40) and \( x + y=6 \) (sum is 6).
From the second equation, we can express \( y = 6 - x \).

Step2: Substitute and solve quadratic equation

Substitute \( y = 6 - x \) into the first equation:
\( x(6 - x)=-40 \)
Expand the left - hand side: \( 6x-x^{2}=-40 \)
Rearrange to standard quadratic form: \( x^{2}-6x - 40=0 \)
Factor the quadratic equation. We need two numbers that multiply to - 40 and add to - 6. The numbers are -10 and 4.
So, \( x^{2}-6x - 40=(x - 10)(x + 4)=0 \)
Set each factor equal to zero:
If \( x - 10=0 \), then \( x = 10 \); if \( x + 4=0 \), then \( x=-4 \)
When \( x = 10 \), \( y=6 - 10=-4 \); when \( x=-4 \), \( y=6-(-4)=10 \)

Answer:

The two numbers are 10 and - 4 (or - 4 and 10).