-15 and 8
To solve this I set up a system of equations. When you add two numbers, let’s say x and y, together you get -7. My first equation is x+y=-7. My second equation is xy=-120, because when you multiply them together you get -120.
x + y =-7
xy = -120
I solved by substitution, so I first got one variable (in this case y) alone on one side of the equation. Let me know if you want me to explain any of these steps further.
x+y = -7
y = -7 - x
I then substituted -7 - x in for y in the other equation.
xy = -120
x(-7 - x) = -120
From here I distributed the x.
-7x -x^2 = -120
-x^2 -7x +120 = 0
-1(x^2 + 7x -120) = 0
-(x-8)(x+15) = 0
x=8,-15
I factored the polynomial to solve for x.
8 + y = -7
y = -15
-15 + y = -7
y = 8
Finally, I solved for y using these values for x. Either way the numbers you get are -15 and 8. To double check this, see that -15+8=-7 and -15(8) =-120
I hope this helps!
