SOLUTION: A rectangle has an area of 34cm. It's length 5 more than twice it's width

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Question 553911: A rectangle has an area of 34cm. It's length 5 more than twice it's width
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangle has an area of 34cm. It's length 5 more than twice it's width
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Area = L*W = 34
L = 2W + 5
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W*(2W+5) = 34
W%5E2+%2B+5W+-+34+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B5x%2B-34+=+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=%285%29%5E2-4%2A1%2A-34=161.

Discriminant d=161 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+161+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+161+%29%29%2F2%5C1+=+3.84428877022476
x%5B2%5D+=+%28-%285%29-sqrt%28+161+%29%29%2F2%5C1+=+-8.84428877022476

Quadratic expression 1x%5E2%2B5x%2B-34 can be factored:
1x%5E2%2B5x%2B-34+=+%28x-3.84428877022476%29%2A%28x--8.84428877022476%29
Again, the answer is: 3.84428877022476, -8.84428877022476. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-34+%29

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W =~ 3.844
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PS it's = it is