SOLUTION: This is my question. The product of two consecutive even integers is 56. Find the two integers. I got this far x(x+2)= 56 x^+2x= 56 x^+2x-56 = 0 (x-?)(x+?)= 0 thanks

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Question 6677: This is my question.
The product of two consecutive even integers is 56. Find the two integers.
I got this far
x(x+2)= 56
x^+2x= 56
x^+2x-56 = 0
(x-?)(x+?)= 0
thanks
Found 2 solutions by xcentaur, ichudov:
Answer by xcentaur(357) About Me  (Show Source):
You can put this solution on YOUR website!
good work on getting this far,
x^+2x-56 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-56+=+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=%282%29%5E2-4%2A1%2A-56=228.

Discriminant d=228 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+228+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+228+%29%29%2F2%5C1+=+6.54983443527075
x%5B2%5D+=+%28-%282%29-sqrt%28+228+%29%29%2F2%5C1+=+-8.54983443527075

Quadratic expression 1x%5E2%2B2x%2B-56 can be factored:
1x%5E2%2B2x%2B-56+=+1%28x-6.54983443527075%29%2A%28x--8.54983443527075%29
Again, the answer is: 6.54983443527075, -8.54983443527075. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-56+%29

Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
great job so far. now you have to solve the quadratic equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-56+=+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=%282%29%5E2-4%2A1%2A-56=228.

Discriminant d=228 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+228+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+228+%29%29%2F2%5C1+=+6.54983443527075
x%5B2%5D+=+%28-%282%29-sqrt%28+228+%29%29%2F2%5C1+=+-8.54983443527075

Quadratic expression 1x%5E2%2B2x%2B-56 can be factored:
1x%5E2%2B2x%2B-56+=+1%28x-6.54983443527075%29%2A%28x--8.54983443527075%29
Again, the answer is: 6.54983443527075, -8.54983443527075. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-56+%29


the answer to this equation is not integer.
so, the answer is that there is no answer to your problem. It is a trick problem.
Think about it, product of consecutive integers 6 and 8 is 48, and for the next two consecutive integers (8 and 10) it is 80.