SOLUTION: The length of a rectangle is 3cm more than 2 times its width. If the area of the rectangle is 93cm2, find the dimensions of the rectangle in numeric values rounded to the nearest

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Question 278388: The length of a rectangle is 3cm more than 2 times its width. If the area of the rectangle is 93cm2, find the dimensions of the rectangle in numeric values rounded to the nearest thousandth of a centimeter
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
l=3+2w
a=lw
a=93
solve for w
93=%283%2B2w%29w
93=3w%2B2w%5E2
0=2w%5E2%2B3w-93
6.1102=w
l=3+2(6.1102)
l=15.2204
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B3x%2B-93+=+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=%283%29%5E2-4%2A2%2A-93=753.

Discriminant d=753 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+753+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+753+%29%29%2F2%5C2+=+6.11021136700612
x%5B2%5D+=+%28-%283%29-sqrt%28+753+%29%29%2F2%5C2+=+-7.61021136700612

Quadratic expression 2x%5E2%2B3x%2B-93 can be factored:
2x%5E2%2B3x%2B-93+=+2%28x-6.11021136700612%29%2A%28x--7.61021136700612%29
Again, the answer is: 6.11021136700612, -7.61021136700612. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B3%2Ax%2B-93+%29