SOLUTION: Find three consecutive even integers such that the product of the first and the third is 18 greater than the product of -1 and the third.

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Question 952370: Find three consecutive even integers such that the product of the first and the third is 18 greater than the product of -1 and the third.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
x=first x+2=second x+4=third
(x)(x+4)=((-1)(x+4))+18
x%5E2%2B4x=-x-4%2B18 Add x to each side.
x%5E2%2B5x=14 Subtract 14 from each side.
x%5E2%2B5x-14=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B5x%2B-14+=+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=%285%29%5E2-4%2A1%2A-14=81.

Discriminant d=81 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+81+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+81+%29%29%2F2%5C1+=+2
x%5B2%5D+=+%28-%285%29-sqrt%28+81+%29%29%2F2%5C1+=+-7

Quadratic expression 1x%5E2%2B5x%2B-14 can be factored:
1x%5E2%2B5x%2B-14+=+1%28x-2%29%2A%28x--7%29
Again, the answer is: 2, -7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-14+%29

ANSWER 1: The first integer is 2.
x+2=2+2=4 ANSWER 2: The second integer is 4.
x+4=2+4=6 ANSWER 3: The third integer is 6.
CHECK:
(2)(6)=-1(6)+18
12=-6+18
12=12