SOLUTION: While finding the amount of seed needed to plant his three square wheat feilds, Hank observed that the side of one feild was 1 kilometer longer than the side of the smallest field

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: While finding the amount of seed needed to plant his three square wheat feilds, Hank observed that the side of one feild was 1 kilometer longer than the side of the smallest field       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 168354: While finding the amount of seed needed to plant his three square wheat feilds, Hank observed that the side of one feild was 1 kilometer longer than the side of the smallest field and that the side of the largest field was 3 kilometers longer than the side of the smallest field. If the total area of the three fields is 38 square kilometers then what is the area of each field.
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
lets call x the side of the small field so other 2 fields will have sides of
x+1 and x+3. total of all these areas will equal 38
:
x%5E2%2B%28x%2B1%29%5E2%2B%28x%2B3%29%5E2=38 multiply this out and end up with
:
3x%5E2%2B8x-28=0 solve by quadratic formula
and you end up with 1 postive answer of 2
:
so areas of the fields are 4,9,25 which equals 38 in total
:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B8x%2B-28+=+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=%288%29%5E2-4%2A3%2A-28=400.

Discriminant d=400 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+400+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+400+%29%29%2F2%5C3+=+2
x%5B2%5D+=+%28-%288%29-sqrt%28+400+%29%29%2F2%5C3+=+-4.66666666666667

Quadratic expression 3x%5E2%2B8x%2B-28 can be factored:
3x%5E2%2B8x%2B-28+=+3%28x-2%29%2A%28x--4.66666666666667%29
Again, the answer is: 2, -4.66666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B8%2Ax%2B-28+%29