SOLUTION: a large rectangular movie screen in an lmax theater has an area of 9,944 square feet. find the dimensions of the screen if it is 25 feet longer it is wide. length=______ft

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Question 317325: a large rectangular movie screen in an lmax theater has an area of 9,944 square feet. find the dimensions of the screen if it is 25 feet longer it is wide.


length=______ft
width=_______ft
Found 2 solutions by JBarnum, solver91311:
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
L=25+W
LW=9944
%2825%2BW%29W=9944
25W%2BW%5E2=9944
W%5E2%2B25W-9944=0
W=88since it cant be negative, see below for solving steps.
L=25%2B88
L=113
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aW%5E2%2BbW%2Bc=0 (in our case 1W%5E2%2B25W%2B-9944+=+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=%2825%29%5E2-4%2A1%2A-9944=40401.

Discriminant d=40401 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-25%2B-sqrt%28+40401+%29%29%2F2%5Ca.

W%5B1%5D+=+%28-%2825%29%2Bsqrt%28+40401+%29%29%2F2%5C1+=+88
W%5B2%5D+=+%28-%2825%29-sqrt%28+40401+%29%29%2F2%5C1+=+-113

Quadratic expression 1W%5E2%2B25W%2B-9944 can be factored:
1W%5E2%2B25W%2B-9944+=+1%28W-88%29%2A%28W--113%29
Again, the answer is: 88, -113. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B25%2Ax%2B-9944+%29

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Solve the quadratic for the short dimension.


John