SOLUTION: A rectangular bedroom is 7ft. longer than it is wide. Its area is 875ft.^2. What are its dimensions?

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Question 199286This question is from textbook algebra and trigonometry
: A rectangular bedroom is 7ft. longer than it is wide. Its area is 875ft.^2. What are its dimensions? This question is from textbook algebra and trigonometry

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=length and w=width
x=w+7
xw=875
w(w+7)=875 substitute w+7 for x.
w^2+7w-875=0
w=26.29... see below
x=33.29...
.
Ed
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B7x%2B-875+=+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=%287%29%5E2-4%2A1%2A-875=3549.

Discriminant d=3549 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+3549+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+3549+%29%29%2F2%5C1+=+26.286742017213
x%5B2%5D+=+%28-%287%29-sqrt%28+3549+%29%29%2F2%5C1+=+-33.286742017213

Quadratic expression 1x%5E2%2B7x%2B-875 can be factored:
1x%5E2%2B7x%2B-875+=+1%28x-26.286742017213%29%2A%28x--33.286742017213%29
Again, the answer is: 26.286742017213, -33.286742017213. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B7%2Ax%2B-875+%29