SOLUTION: The area of a rectangular tabletop is 6 square feet. If the width is 2 feet shorter than the length, then what are the dimensions?

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Question 286170: The area of a rectangular tabletop is 6 square feet. If the width is 2 feet shorter than the length, then what are the dimensions?
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
L = length
W = width
A = area = L*W = 6 sq. ft
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L = W+2
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Substituting...
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(W+2)*W = 6
W^2 + 2W = 6
W^2 + 2W -6 =0
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We cannot factor it, so use the quadratic equation...
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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%2B2x%2B-6+=+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=%282%29%5E2-4%2A1%2A-6=28.

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

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+28+%29%29%2F2%5C1+=+1.64575131106459
x%5B2%5D+=+%28-%282%29-sqrt%28+28+%29%29%2F2%5C1+=+-3.64575131106459

Quadratic expression 1x%5E2%2B2x%2B-6 can be factored:
1x%5E2%2B2x%2B-6+=+1%28x-1.64575131106459%29%2A%28x--3.64575131106459%29
Again, the answer is: 1.64575131106459, -3.64575131106459. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-6+%29

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A negative width is nonsensical, so we'll go with W = approximately 1.6457.
Substituting W=1.6457, we can find L.
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L = W+2 = 1.6457 + 2 = 3.6457
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Checking this solution, is the Area = 6?
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1.6457*3.6457 =5.9997, which within the rounding error caused by using the approximation W = 1.6457.
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Done.