SOLUTION: Ok, the problem below I just can't figure out! Can you please help me? can you show me how to get the answer? The area of a rectangle is 80 square feet and its length is 1 foot m

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Question 191065: Ok, the problem below I just can't figure out! Can you please help me? can you show me how to get the answer?
The area of a rectangle is 80 square feet and its length is 1 foot more than its width. Find its width.
Thank you for your time!
G.E.P
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Ok, the problem below I just can't figure out! Can you please help me? can you show me how to get the answer?
The area of a rectangle is 80 square feet and its length is 1 foot more than its width. Find its width.
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Area = l*w
A = w*(w+1) = 80
w%5E2+%2B+w+-+80+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-80+=+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=%281%29%5E2-4%2A1%2A-80=321.

Discriminant d=321 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+321+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+321+%29%29%2F2%5C1+=+8.45823643358446
x%5B2%5D+=+%28-%281%29-sqrt%28+321+%29%29%2F2%5C1+=+-9.45823643358446

Quadratic expression 1x%5E2%2B1x%2B-80 can be factored:
1x%5E2%2B1x%2B-80+=+%28x-8.45823643358446%29%2A%28x--9.45823643358446%29
Again, the answer is: 8.45823643358446, -9.45823643358446. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-80+%29


Use the positive value.