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

Answer 1

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.

Answer 2

To find two numbers that multiply to -120 and add up to -14, we need to solve a system of equations. Let's call the two numbers x and y. We have the equations xy = -120 and x + y = -14. By factoring -120, we get the pairs of factors: (1, -120), (2, -60), (3, -40), (4, -30), (5, -24), (6, -20), (8, -15), and (10, -12). Among these pairs, the numbers that add up to -14 are -10 and 12. So, the two numbers are -10 and 12.

Answer 3

Well, well, well, aren't we playing detective now? The two numbers you're looking for are -20 and 6. They multiply to -120 and add up to -14. Case closed!

Answer 4

-20 and -6