SOLUTION: I believe this one needs the quadratic formula but I'm not entirely sure how I would set it up and solve. In order to grow all the peppers he needs, Joe needs to double the siz

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Question 793312: I believe this one needs the quadratic formula but I'm not entirely sure how I would set it up and solve.
In order to grow all the peppers he needs, Joe needs to double the size of his garden.He plans to extend his garden by adding a uniform strip to each side of the current 6ft by 8ft rectangular plot. how wide does the strip need to be?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
In order to grow all the peppers he needs, Joe needs to double the size of his garden.He plans to extend his garden by adding a uniform strip to each side of the current 6ft by 8ft rectangular plot. how wide does the strip need to be?
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If you mean each of the 4 sides:
width = x --> Area of (6 + 2x)*(8 + 2x) = 2*48
(x + 3)*(x + 4) = 24
x%5E2+%2B+7x+-+12+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B7x%2B-12+=+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-12=97.

Discriminant d=97 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+97+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+97+%29%29%2F2%5C1+=+1.42442890089805
x%5B2%5D+=+%28-%287%29-sqrt%28+97+%29%29%2F2%5C1+=+-8.42442890089805

Quadratic expression 1x%5E2%2B7x%2B-12 can be factored:
1x%5E2%2B7x%2B-12+=+%28x-1.42442890089805%29%2A%28x--8.42442890089805%29
Again, the answer is: 1.42442890089805, -8.42442890089805. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B7%2Ax%2B-12+%29

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width =~ 1.1244 feet