What are the two numbers that if I multiply I get -180 but if I add I get 7
To find the two numbers, let's assume the two numbers as x and y.
According to the problem, we have two equations:
1. xy = -180 (product of the two numbers is -180)
2. x + y = 7 (sum of the two numbers is 7)
Now, we can solve these equations simultaneously to find the values of x and y.
First, let's rearrange the second equation to solve for one variable in terms of the other:
x = 7 - y
Substituting this value of x into the first equation:
(7 - y) * y = -180
Expanding the equation:
7y - y^2 = -180
Rearranging the equation:
y^2 - 7y - 180 = 0
Now, we can factorize this quadratic equation:
(y - 20)(y + 9) = 0
Setting each factor to zero and solving for y:
y - 20 = 0 --> y = 20
or
y + 9 = 0 --> y = -9
So the two possible values for y are 20 and -9.
Now, substituting these values of y back into the equation x = 7 - y, we can find the corresponding values of x.
For y = 20:
x = 7 - 20
x = -13
For y = -9:
x = 7 - (-9)
x = 7 + 9
x = 16
Therefore, the two numbers are -13 and 20, or 16 and -9.