What do numbers if i multiply I will get -180 but when added up I get 7
The two numbers that satisfy these conditions are 15 and -12.
When multiplied, 15 x -12 = -180.
When added, 15 + (-12) = 3.
To find the numbers that, when multiplied, give -180 and, when added, give 7, we can use algebraic equations.
Let's assume the two numbers are x and y.
We can set up two equations based on the given information:
1) xy = -180 (The product of the numbers is -180)
2) x + y = 7 (The sum of the numbers is 7)
Let's solve these equations step-by-step:
From equation 2), we can rewrite it as y = 7 - x.
Now, substitute this value of y in equation 1):
x(7 - x) = -180
Distribute the x:
7x - x^2 = -180
Rearrange the equation in the standard form:
x^2 - 7x - 180 = 0
This is a quadratic equation. We can solve it by factoring or using the quadratic formula. Let's use factoring:
(x - 20)(x + 9) = 0
Setting each factor equal to zero, we get:
x - 20 = 0 or x + 9 = 0
Solving for x, we have two possible values:
x = 20 or x = -9
Now substitute these values of x into equation 2) to find the values of y:
For x = 20:
y = 7 - x
y = 7 - 20
y = -13
So, one pair of numbers is 20 and -13.
For x = -9:
y = 7 - x
y = 7 - (-9)
y = 16
So, the other pair of numbers is -9 and 16.
Therefore, the two pairs of numbers that multiply to -180 and add up to 7 are:
1) 20 and -13
2) -9 and 16