SOLUTION: The area of a rectangle is six square feet. The rectangle's length is two feet more than three times the width. Find the rectangle's width (in feet) rounded to two decimal places

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Question 993342: The area of a rectangle is six square feet. The rectangle's length is two feet more than three times the width. Find the rectangle's width (in feet) rounded to two decimal places
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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W=width; L=length=3W+2
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A=LW
A=(3W+2)(W)
6=3W^2+2W
0=3W^2+2W-6
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aW%5E2%2BbW%2Bc=0 (in our case 3W%5E2%2B2W%2B-6+=+0) has the following solutons:

W%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%2A3%2A-6=76.

Discriminant d=76 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+76+%29%29%2F2%5Ca.

W%5B1%5D+=+%28-%282%29%2Bsqrt%28+76+%29%29%2F2%5C3+=+1.11963298118022
W%5B2%5D+=+%28-%282%29-sqrt%28+76+%29%29%2F2%5C3+=+-1.78629964784689

Quadratic expression 3W%5E2%2B2W%2B-6 can be factored:
3W%5E2%2B2W%2B-6+=+3%28W-1.11963298118022%29%2A%28W--1.78629964784689%29
Again, the answer is: 1.11963298118022, -1.78629964784689. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B2%2Ax%2B-6+%29

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W=1.12 feet
ANSWER: The width is 1.12 feet
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CHECK:
L=3W+2=3(1.12)+2=3.36+2=5.36
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A=LW
6=(5.36)(1.12)
6=6