SOLUTION: You have a pool that measure 15 yards by 10 yards. You want to build a deck around all four sides of the pool and you want to increase the total area to 250 square yards. What

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Question 246796:
You have a pool that measure 15 yards by 10 yards. You want to build a deck around all four sides of the pool and you want to increase the total area to 250 square yards. What is the width of the deck?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
15*10=150 sq. yds
(15+a)(10+a)=250
150+15a+a^2=250
a^2+25a=100
we can't use the negative amount
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B25x%2B-100+=+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=%2825%29%5E2-4%2A1%2A-100=1025.

Discriminant d=1025 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-25%2B-sqrt%28+1025+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2825%29%2Bsqrt%28+1025+%29%29%2F2%5C1+=+3.50781059358212
x%5B2%5D+=+%28-%2825%29-sqrt%28+1025+%29%29%2F2%5C1+=+-28.5078105935821

Quadratic expression 1x%5E2%2B25x%2B-100 can be factored:
1x%5E2%2B25x%2B-100+=+1%28x-3.50781059358212%29%2A%28x--28.5078105935821%29
Again, the answer is: 3.50781059358212, -28.5078105935821. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B25%2Ax%2B-100+%29

solve for a
a is about 3.5078
so now we have 15+3.5078 and 10+3.5078
13.5078