SOLUTION: the length of a rectangle is 15 more than its width. find its length when its area is 150cm^2

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Question 885326: the length of a rectangle is 15 more than its width. find its length when its area is 150cm^2
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
A = Lw = (15+w)w = 150cm^2
w^2 + 15w - 150 = 0 (Tossing out the negative solution for unit measure)
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B15x%2B-150+=+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=%2815%29%5E2-4%2A1%2A-150=825.

Discriminant d=825 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-15%2B-sqrt%28+825+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2815%29%2Bsqrt%28+825+%29%29%2F2%5C1+=+6.86140661634507
x%5B2%5D+=+%28-%2815%29-sqrt%28+825+%29%29%2F2%5C1+=+-21.8614066163451

Quadratic expression 1x%5E2%2B15x%2B-150 can be factored:
1x%5E2%2B15x%2B-150+=+1%28x-6.86140661634507%29%2A%28x--21.8614066163451%29
Again, the answer is: 6.86140661634507, -21.8614066163451. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B15%2Ax%2B-150+%29