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.
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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.
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!
Oh, dude, you're hitting me with some math vibes! So, the two numbers we're looking for are -12 and -10. They multiply to 120 and add up to -14. It's like a math puzzle, but with numbers instead of jigsaw pieces.
The original number is 14.
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Multiply by 3 for one number. Then add 5 for the next number.
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