What 2 number multiply to -120 and add up to -14?

This is algebra.

Let's take 2 numbers, x and y. What we want is xy = -120 and x+y = -14.

So we have two equations. Let's solve for one of the numbers and move that over to the other equation.

x+y=-14

x=-14-y

Let us now plug that x into the other equation.

(-14-y)y=-120

We now distribute the y to both -14 and -y.

-14y-y^2=-120

moving everything to one side we get

0=y^2+14y-120

now it's just a matter of solving for y, which can be found using the quadratic equation (-b+-(b^2-4ac)^(1/2))/(2a), where a=1, b=14, and c=-120.

Let's try plus first

(-14+(14^2-(4)(-120))^(1/2))/2

(-14+(196+480)^(1/2))/2

(-14+26)/2

6

so y=6. Let's plug that into one of the equations we had, x+y=-14.

x+6=-14

x=-20

To see if this works, let's try y=6 and x=-20 on both equations

-20(6)=-120

-20+6=-14

They work!

By the way, if we had tried minus in the quadratic equation, we would've gotten -20 for y and x as 6.