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