SOLUTION: a rectangular skating rink measures 40 by 20. it is to be doubled in area by extending each side by the same amount. determine how much each side should be extended to the nearest

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Question 448374: a rectangular skating rink measures 40 by 20. it is to be doubled in area by extending each side by the same amount. determine how much each side should be extended to the nearest meter.
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
40x20=800
(40+2x)(20+2x)=1600
800+120x+4x2=1600
4x2+120x-800=0
x2+30x-200=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B30x%2B-200+=+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=%2830%29%5E2-4%2A1%2A-200=1700.

Discriminant d=1700 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-30%2B-sqrt%28+1700+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2830%29%2Bsqrt%28+1700+%29%29%2F2%5C1+=+5.6155281280883
x%5B2%5D+=+%28-%2830%29-sqrt%28+1700+%29%29%2F2%5C1+=+-35.6155281280883

Quadratic expression 1x%5E2%2B30x%2B-200 can be factored:
1x%5E2%2B30x%2B-200+=+1%28x-5.6155281280883%29%2A%28x--35.6155281280883%29
Again, the answer is: 5.6155281280883, -35.6155281280883. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B30%2Ax%2B-200+%29

Throwing out the negative answer, we get x=5.61552812, which is the amount to be added to all 4 sides..