SOLUTION: For the problem given below, set up an equation and solve. Show all work (including what your variables represent), detailing each step, to ensure that I am able to follow your wo

Algebra ->  Linear-equations -> SOLUTION: For the problem given below, set up an equation and solve. Show all work (including what your variables represent), detailing each step, to ensure that I am able to follow your wo      Log On


   

Question 941776: For the problem given below, set up an equation and solve. Show all work (including what your variables represent), detailing each step, to ensure that I am able to follow your work. Clearly state your solution. Please and thank you
The problem:
If the product of two consecutive positive even integers is equal to 168, then what are the integers.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Two consecutive even integers, I and I+2
Product is 168, (I)(I+2)=168
I%5E2%2B2I=168 Subtract 168 from each side
I%5E2%2B2I-168=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aI%5E2%2BbI%2Bc=0 (in our case 1I%5E2%2B2I%2B-168+=+0) has the following solutons:

I%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-168=676.

Discriminant d=676 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+676+%29%29%2F2%5Ca.

I%5B1%5D+=+%28-%282%29%2Bsqrt%28+676+%29%29%2F2%5C1+=+12
I%5B2%5D+=+%28-%282%29-sqrt%28+676+%29%29%2F2%5C1+=+-14

Quadratic expression 1I%5E2%2B2I%2B-168 can be factored:
1I%5E2%2B2I%2B-168+=+1%28I-12%29%2A%28I--14%29
Again, the answer is: 12, -14. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-168+%29

The results are 12 and -14. The integer specified is positive, so I=12 and the second is I+2=14
CHECK:the product of 12 and 14 is (12)(14}=168
The ANSWER (SOLUTION) Is 12 and 14