SOLUTION: A rectangular movie screen has an area of 9,315 square feet. Find the dimensions of the screen if it is 18 feet longer than it is wide.

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Question 444500: A rectangular movie screen has an area of 9,315 square feet. Find the dimensions of the screen if it is 18 feet longer than it is wide.
Answer by chriswen(106) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the width.
Let x + 18 be the length.
...
A=l*w
9315=(x+18)(x)
9315=x^2+18x
0=x^2+18x-9315
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B18x%2B-9315+=+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=%2818%29%5E2-4%2A1%2A-9315=37584.

Discriminant d=37584 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-18%2B-sqrt%28+37584+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2818%29%2Bsqrt%28+37584+%29%29%2F2%5C1+=+87.9329665284211
x%5B2%5D+=+%28-%2818%29-sqrt%28+37584+%29%29%2F2%5C1+=+-105.932966528421

Quadratic expression 1x%5E2%2B18x%2B-9315 can be factored:
1x%5E2%2B18x%2B-9315+=+1%28x-87.9329665284211%29%2A%28x--105.932966528421%29
Again, the answer is: 87.9329665284211, -105.932966528421. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B18%2Ax%2B-9315+%29

...
So, x is the positive number as we are dealing with positive values.
x=87.9329665284211
x+18=105.9329665284211
So therefore, the rectangle movie screen is roughly 88 ft by 106 ft.