what two numbers have a product of 12 and the sum of -7

Answer 1

Use a system of equations with the information you're provided. Our two numbers will be represented by X and Y.

XY = 12

X + Y = -7

Lets solve for one letter in an equation and input it into the opposing equation. The second equation is easier to read and solve for one letter. What you do to the left side of the equal sign, you must do to the right side of the equal sign. When we move a number or variable to the other side, we use its opposite calculation. Plus, we subtract. Multiply, we divide. etc.

X + Y - Y = -7 - Y

X = -7 - Y

Then plug the formula for X into the first equation from the prior step.

(-7 - Y)Y = 12

-7Y - Y² = 12

In order to solve for Y, we have a quadratic formula. If we set it equal to 0, we can find two numbers when breaking it down.

-Y² - 7Y - 12 = 0

-1(Y² + 7Y + 12) = 0(-1) Pulled out the negative to make it easier to read.

Y² + 7Y + 12 = 0

(Y + 3) (Y + 4) = 0

Y = -3 or Y = -4

To check these numbers:

(-3)(-4) = 12

(-3) + (-4) = -7

Answer 2

x-y=12

x+y=-7

-4, -3