SOLUTION: The area of a rectangle is 33m^2, and the length of the rectangle is 5 m less than double the width. Find the dimensions of the rectangle

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Question 874852: The area of a rectangle is 33m^2, and the length of the rectangle is 5 m less than double the width. Find the dimensions of the rectangle
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
A = Lw = 33m^2
(2w-5)w = 33
2w^2 - 5w - 33 = 0, w = 5.5m and L = 6m
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-5x%2B-33+=+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=%28-5%29%5E2-4%2A2%2A-33=289.

Discriminant d=289 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+289+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+289+%29%29%2F2%5C2+=+5.5
x%5B2%5D+=+%28-%28-5%29-sqrt%28+289+%29%29%2F2%5C2+=+-3

Quadratic expression 2x%5E2%2B-5x%2B-33 can be factored:
2x%5E2%2B-5x%2B-33+=+2%28x-5.5%29%2A%28x--3%29
Again, the answer is: 5.5, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-5%2Ax%2B-33+%29