SOLUTION: A rectangular sheet of paper has an area of 204in. squared. Its dimensions are (x+4) by (x+9). What are the dimensions of the paper. Thank You

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Question 440412: A rectangular sheet of paper has an area of 204in. squared. Its dimensions are (x+4) by (x+9). What are the dimensions of the paper.
Thank You
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangular sheet of paper has an area of 204in. squared. Its dimensions are (x+4) by (x+9). What are the dimensions of the paper.
.
since area is width times length:
204 = (x+4)(x+9)
FOIL the right:
204 = x^2+9x+4x+36
204 = x^2+13x+36
0 = x^2+13x-170
solve by applying the quadratic formula to get:
x = {8.1, -21.1}
throw out the negative solution leaving:
x = 8.1
.
dimensions are:
12.1 inch by 17.1 inch
.
details of quadratic follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B13x%2B-170+=+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=%2813%29%5E2-4%2A1%2A-170=849.

Discriminant d=849 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-13%2B-sqrt%28+849+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2813%29%2Bsqrt%28+849+%29%29%2F2%5C1+=+8.06880228433347
x%5B2%5D+=+%28-%2813%29-sqrt%28+849+%29%29%2F2%5C1+=+-21.0688022843335

Quadratic expression 1x%5E2%2B13x%2B-170 can be factored:
1x%5E2%2B13x%2B-170+=+1%28x-8.06880228433347%29%2A%28x--21.0688022843335%29
Again, the answer is: 8.06880228433347, -21.0688022843335. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B13%2Ax%2B-170+%29