SOLUTION: I need your help with this question. A farmer has 2420 feet of fence to enclose a rectangular area that borders a river. No fence is needed along the river. Find the possibe dimens

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Question 435606: I need your help with this question. A farmer has 2420 feet of fence to enclose a rectangular area that borders a river. No fence is needed along the river. Find the possibe dimensions to enclose +435600+feet%5E2+. I have two equations which are x+x+y=2420 and xy=435600 and I can't figure out where to go from there.
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
2x+y=2420
xy=435600
.
y=435600/x
2x+(435600/x)=2420
2x^2+435600=2420x
2x^2-2420x+435600=0
x^2-1210x+217800=0
x=990, y=220 or vice versa (see below)
.
Ed
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1210x%2B217800+=+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=%28-1210%29%5E2-4%2A1%2A217800=592900.

Discriminant d=592900 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1210%2B-sqrt%28+592900+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1210%29%2Bsqrt%28+592900+%29%29%2F2%5C1+=+990
x%5B2%5D+=+%28-%28-1210%29-sqrt%28+592900+%29%29%2F2%5C1+=+220

Quadratic expression 1x%5E2%2B-1210x%2B217800 can be factored:
1x%5E2%2B-1210x%2B217800+=+1%28x-990%29%2A%28x-220%29
Again, the answer is: 990, 220. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1210%2Ax%2B217800+%29