What two numbers multiply together to equal 16 and add together to equal -2?

None, because both numbers must be negative in order to get a positive answer, or both positive. However, -2 means that there is at least one negative number, or two negative numbers. the only option : -1+(-1)= -2. So there is no real solution.

Answered by joannashutt | 2024-06-10

There is a solution, but you might not have learned how to do it yet in middle school.
If you've learned to use the quadratic formula to solve a quadratic equations, then you can do this.
The first requirement says: ' x ' times ' y ' = 16 The second requirement says: (x + y) = -2
Take the second requirement, and subtract ' x ' from each side:
y = -x - 2
Substitute this into the first requirement:
' x ' times (-x - 2) = 16
Eliminate parentheses:
-x² - 2x = 16
Subtract 16 from each side:
-x² - 2x - 16 = 0
Multiply each side by -1:
x² + 2x + 16 = 0
Solve this with the quadratic formula, and you get two solutions, which are the two numbers that satisfy both requirements.
The numbers are
-1 + √-15
-1 - √-15
Check:
-- Product: (-1 + √-15) times (-1 - √-15) = 1 + 15 = 16
-- Sum = -1 + √-15 -1 - √-15 = -2
They work. yay

Answered by AL2006 | 2024-06-24

Two numbers that multiply to 16 and add to -2 are complex numbers: − 1 + i 15 ​ and − 1 − i 15 ​ . These solutions arise from solving a quadratic equation that results from the initial conditions. They satisfy both the product and sum requirements given in the question.
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Answered by AL2006 | 2024-09-27