SOLUTION: A rectangle measures 24ft by 32ft. The length and width of the floor will both be increased by X feet. Write and equation that can be used to determine the value of X, in feet, if

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Question 445185: A rectangle measures 24ft by 32ft. The length and width of the floor will both be increased by X feet. Write and equation that can be used to determine the value of X, in feet, if the area of the new dance floor is 1,174.25 sg ft. What are the new dimensions of the floor?
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B24%29%28x%2B32%29+=+1174.25
x%5E2+%2B+56x+%2B+768+=+1174.25
x%5E2+%2B+56x+-406.25+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B56x%2B-406.25+=+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=%2856%29%5E2-4%2A1%2A-406.25=4761.

Discriminant d=4761 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-56%2B-sqrt%28+4761+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2856%29%2Bsqrt%28+4761+%29%29%2F2%5C1+=+6.5
x%5B2%5D+=+%28-%2856%29-sqrt%28+4761+%29%29%2F2%5C1+=+-62.5

Quadratic expression 1x%5E2%2B56x%2B-406.25 can be factored:
1x%5E2%2B56x%2B-406.25+=+1%28x-6.5%29%2A%28x--62.5%29
Again, the answer is: 6.5, -62.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B56%2Ax%2B-406.25+%29


So our positive answer is 6.5. This means that the length and width has been increased by 6.5 ft.
Then L = x+24
L = 6.5 + 24
L = 30.5
========
W = x+32
W = 6.5 + 32
W = 38.5
The new dimensions are 30.5 x 38.5.