Final Answer:
The two numbers that give you -36 when multiplying but when adding them give you 16 are 6 and -6.
Step-by-step explanation:
Let x and y be the two numbers we are looking for. We know that xy = -36 and x + y = 16.
From the second equation, we can express y in terms of x:
y = 16 - x
Substituting this expression for y into the first equation, we get:
x(16 - x) = -36
Expanding this expression, we get:
16x - x² = -36
Moving all terms to one side, we get:
x² - 16x + 36 = 0
Factoring this expression, we get:
(x - 6)(x - 6) = 0
Therefore, x = 6. Substituting this value of x back into the equation y = 16 - x, we get:
y = 16 - 6 = 10
Therefore, the two numbers that give you -36 when multiplying but when adding them give you 16 are 6 and 10.