SOLUTION: If the sum of 2 numbers is -14 and their product is 32, what are the numbers? Let x = one number Let x - 14 = the other number x(x - 14) = 32 x^2- 14x + 32 (x - 6) (x-8)

Algebra ->  Human-and-algebraic-language -> SOLUTION: If the sum of 2 numbers is -14 and their product is 32, what are the numbers? Let x = one number Let x - 14 = the other number x(x - 14) = 32 x^2- 14x + 32 (x - 6) (x-8)      Log On


   

Question 396646: If the sum of 2 numbers is -14 and their product is 32, what are the numbers?
Let x = one number
Let x - 14 = the other number
x(x - 14) = 32
x^2- 14x + 32
(x - 6) (x-8)
The two numbers are -8 and -6
I know that -8 + -6 = -14 but when I plug in the numbers that do not equal 32. What am I not doing correct?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If the sum of 2 numbers is -14 and their product is 32, what are the numbers?
Let x = one number
Let x - 14 = the other number
x(x - 14) = 32
x^2- 14x + 32
(x - 6) (x-8)
The two numbers are -8 and -6
I know that -8 + -6 = -14 but when I plug in the numbers that do not equal 32. What am I not doing correct?
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Let x = one number
Let -14 - x = the other number
x(-x - 14) = 32
-x^2 - 14x - 32 = 0
x^2 + 14x + 32 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B14x%2B32+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2814%29%5E2-4%2A1%2A32=68.

Discriminant d=68 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-14%2B-sqrt%28+68+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2814%29%2Bsqrt%28+68+%29%29%2F2%5C1+=+-2.87689437438234
x%5B2%5D+=+%28-%2814%29-sqrt%28+68+%29%29%2F2%5C1+=+-11.1231056256177

Quadratic expression 1x%5E2%2B14x%2B32 can be factored:
1x%5E2%2B14x%2B32+=+%28x--2.87689437438234%29%2A%28x--11.1231056256177%29
Again, the answer is: -2.87689437438234, -11.1231056256177. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B14%2Ax%2B32+%29

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x = -7 ± sqrt(17)
One number is -7 + sqrt, the other is -7 - sqrt
No integer solutions.
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I would check for a typo.
If the sum is -12, then it's -4 and -8.