SOLUTION: Hi, I was hoping to get help with the formula to solve this quadratic equation problem. A cement walk of a constant width is built around a 20 ft by 40 ft rectangular pool. The t

Algebra ->  Formulas -> SOLUTION: Hi, I was hoping to get help with the formula to solve this quadratic equation problem. A cement walk of a constant width is built around a 20 ft by 40 ft rectangular pool. The t      Log On


   

Question 279301: Hi, I was hoping to get help with the formula to solve this quadratic equation problem.
A cement walk of a constant width is built around a 20 ft by 40 ft rectangular pool. The total area of the pool and the walk is 1500 sq ft.Find the width of the walk.
Thank you
Erin
deae8286@hotmail.com
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
well %2820%2B2w%29%2840%2B2w%29=1500 w=width of sidewalk
%28800%2B80w%2B20w%2B4w%5E2%29=1500
800%2B100w%2B4w%5E2=1500
-700%2B100w%2B4w%5E2=0
4%28-175%2B25w%2Bw%5E2%29=0
w=5.7002747232013
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B25x%2B-175+=+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-175=1325.

Discriminant d=1325 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-25%2B-sqrt%28+1325+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2825%29%2Bsqrt%28+1325+%29%29%2F2%5C1+=+5.7002747232013
x%5B2%5D+=+%28-%2825%29-sqrt%28+1325+%29%29%2F2%5C1+=+-30.7002747232013

Quadratic expression 1x%5E2%2B25x%2B-175 can be factored:
1x%5E2%2B25x%2B-175+=+1%28x-5.7002747232013%29%2A%28x--30.7002747232013%29
Again, the answer is: 5.7002747232013, -30.7002747232013. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B25%2Ax%2B-175+%29