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 know that \( xy=- 40\) and \(x + y=6\). From the second equation, we can express \(y = 6 - x\).

Step2: Substitute and solve the quadratic equation

Substitute \(y = 6 - x\) into \(xy=-40\):
\(x(6 - x)=-40\)
Expand the left - hand side: \(6x-x^{2}=-40\)
Rearrange the equation to standard quadratic form \(ax^{2}+bx + c = 0\): \(x^{2}-6x - 40=0\)
Factor the quadratic equation. We need two numbers that multiply to \(-40\) and add up to \(-6\). The numbers are \(-10\) and \(4\) since \((-10)\times4=-40\) and \(-10 + 4=-6\). So, \(x^{2}-6x - 40=(x - 10)(x+4)=0\)
Set each factor equal to zero:
If \(x - 10=0\), then \(x = 10\) and \(y=6 - 10=-4\)
If \(x + 4=0\), then \(x=-4\) and \(y=6-(-4)=10\)

Answer:

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