Question

Write two numbers that multiply to the value on top and add to the value on bottom

16

-8

Answer 1

To find two numbers that multiply to 16 and add to -8, we can denote the two numbers as \( x \) and \( y \). Therefore, we have:

1. \( x \cdot y = 16 \)
2. \( x + y = -8 \)

To solve for \( x \) and \( y \), we can express \( y \) in terms of \( x \):

\( y = -8 - x \)

Now, substitute this into the first equation:

\( x(-8 - x) = 16 \)

Expanding this gives:

\( -8x - x^2 = 16 \)

Rearranging the equation:

\( x^2 + 8x + 16 = 0 \)

This can be factored as:

\( (x + 4)(x + 4) = 0 \)

Thus, the solution is:

\( x + 4 = 0 \rightarrow x = -4 \)

Then, substituting \( x \) back to find \( y \):

\( y = -8 - (-4) = -4 \)

So the two numbers are \( -4 \) and \( -4 \).

In conclusion, the two numbers that multiply to 16 and add to -8 are:

**-4 and -4**.