SOLUTION: I need to understand the process and show and explain EACH step in setting up and solving the following application problems. Give answers to the nearest thousandth. Thank you for

Algebra ->  Square-cubic-other-roots -> SOLUTION: I need to understand the process and show and explain EACH step in setting up and solving the following application problems. Give answers to the nearest thousandth. Thank you for       Log On


   

Question 41056: I need to understand the process and show and explain EACH step in setting up and solving the following application problems. Give answers to the nearest thousandth. Thank you for you help.

b. If the length of a rectangle is 3 ft. less than twice its width and the area of the rectangle is 66 square feet, what are the dimensions of the rectangle?

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
The width is defined as: w
The length is defined as: 2w+-+3
Length * Width = Area
%282w+-+3%29%28w%29+=+66
2w%5E2+-+3w+-+66+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aw%5E2%2Bbw%2Bc=0 (in our case 2w%5E2%2B-3w%2B-66+=+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=%28-3%29%5E2-4%2A2%2A-66=537.

Discriminant d=537 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+537+%29%29%2F2%5Ca.

w%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+537+%29%29%2F2%5C2+=+6.54331511312823
w%5B2%5D+=+%28-%28-3%29-sqrt%28+537+%29%29%2F2%5C2+=+-5.04331511312823

Quadratic expression 2w%5E2%2B-3w%2B-66 can be factored:
2w%5E2%2B-3w%2B-66+=+2%28w-6.54331511312823%29%2A%28w--5.04331511312823%29
Again, the answer is: 6.54331511312823, -5.04331511312823. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-3%2Ax%2B-66+%29

w+=+6.543
l+=+10.086