what numbers add up to -12, but they multiply to 27
-3 , -9
To find two numbers that add up to -12 and multiply to 27, we can use a system of equations.
Let's assume the two numbers are x and y.
According to the given condition, we can write two equations:
Equation 1: x + y = -12
Equation 2: x * y = 27
To solve this system of equations, we can use the substitution method. Solve Equation 1 for x:
x = -12 - y
Now substitute this expression for x in Equation 2:
(-12 - y) * y = 27
Expanding the equation, we get:
-12y - y^2 = 27
Rearranging the equation, we get:
y^2 + 12y + 27 = 0
This quadratic equation can be factored:
(y + 9) (y + 3) = 0
Setting each factor to zero, we solve for y:
y + 9 = 0 -> y = -9
y + 3 = 0 -> y = -3
Now substitute these values of y back into Equation 1 to find the corresponding values of x:
For y = -9: x = -12 - (-9) = -12 + 9 = -3
For y = -3: x = -12 - (-3) = -12 + 3 = -9
Therefore, the two numbers that add up to -12 and multiply to 27 are -3 and -9.
To find two numbers that add up to -12 but multiply to 27, we can start by considering the factors of 27. The factors of 27 are 1, 3, 9, and 27. Let's go through the possible combinations to see if any of them add up to -12.
1 + 27 = 28
3 + 9 = 12
9 + 3 = 12
27 + 1 = 28
None of these combinations add up to -12. However, we can also consider negative numbers as factors since multiplying negative numbers gives a positive result. Let's try considering the negative factors as well.
-1 + -27 = -28
-3 + -9 = -12
-9 + -3 = -12
-27 + -1 = -28
Here we have two combinations that add up to -12: -3 and -9. These two numbers also multiply to 27. Therefore, the numbers that satisfy the given conditions are -3 and -9.