Question

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

Explanation:

Step1: Define variables

Let the two numbers be \( x \) and \( y \). We know that \( xy=-40 \) and \( x + y=6 \).

Step2: Express one variable

From \( x + y=6 \), we can express \( y = 6 - x \).

Step3: Substitute into product equation

Substitute \( y = 6 - x \) into \( xy=-40 \):
\( x(6 - x)=-40 \)
Expand: \( 6x-x^{2}=-40 \)
Rearrange to standard quadratic form: \( x^{2}-6x - 40=0 \)

Step4: Factor the quadratic

Factor \( x^{2}-6x - 40 \). We need two numbers that multiply to - 40 and add to - 6. The numbers are - 10 and 4.
So, \( x^{2}-6x - 40=(x - 10)(x + 4)=0 \)

Step5: Solve for x

Set each factor equal to zero:
\( x - 10 = 0\) gives \( x = 10 \)
\( x + 4=0\) gives \( x=-4 \)

Step6: Find corresponding y

If \( x = 10 \), then \( y=6 - 10=-4 \)
If \( x=-4 \), then \( y=6-(-4)=10 \)

Answer:

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