To find two numbers that multiply to 36 and add to -20, we can use a system of equations:
Let x be one of the numbers and y be the other number.
From the problem, we know that:
x * y = 36 (equation 1)
x + y = -20 (equation 2)
We can solve this system of equations by using substitution or elimination.
Using substitution, we can solve equation 2 for x or y:
x + y = -20
x = -20 - y
Substituting this expression for x into equation 1, we get:
(-20 - y) * y = 36
Expanding the left side gives:
-y^2 - 20y = 36
Moving all the terms to one side gives:
-y^2 - 20y - 36 = 0
Multiplying both sides by -1 gives:
y^2 + 20y + 36 = 0
We can factor this quadratic equation as:
(y + 18) (y + 2) = 0
Therefore, the two possible values for y are -18 and -2.
Substituting each value of y back into equation 2, we can find the corresponding value of x:
If y = -18, then x = -20 - (-18) = -2
If y = -2, then x = -20 - (-2) = -18
Therefore, the two numbers that multiply to 36 and add to -20 are -18 and -2.