Answer:
Let's call the two numbers we need to find "x" and "y". We know that:
- x times y equals 36
- x plus y equals -20
To solve for x and y, we can use a system of equations. We can start by using the first equation to solve for one of the variables in terms of the other. Let's solve for y:
x times y equals 36
y equals 36 divided by x
Now we can substitute this expression for y into the second equation and solve for x:
x plus y equals -20
x plus (36 divided by x) equals -20
Multiplying both sides of the equation by x gives us:
x² + 36 = -20x
Moving all the terms to one side gives us:
x² + 20x + 36 = 0
We can factor this quadratic equation to get:
(x + 2)(x + 18) = 0
So either x + 2 = 0 or x + 18 = 0. This gives us two possible values for x:
- x = -2, which means y = 36/-2 = -18
- x = -18, which means y = 36/-18 = -2
So the two numbers that multiply to 36 and add up to -20 are -2 and -18.
Explanation