SOLUTION: A 10 by 14 meter garden will have a sidewalk of width x along the two 14 meter sides and width 2x along the two 10 meter sides. Approximate (to the nearest hundredths) the value of

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A 10 by 14 meter garden will have a sidewalk of width x along the two 14 meter sides and width 2x along the two 10 meter sides. Approximate (to the nearest hundredths) the value of      Log On


   

Question 849083: A 10 by 14 meter garden will have a sidewalk of width x along the two 14 meter sides and width 2x along the two 10 meter sides. Approximate (to the nearest hundredths) the value of x that will make the area covered by sidewalks and the garden total 174 Square meters. (My teacher said to use the quadratic formula as well)
So I did (4x+10)(2x+14)=174 Ending up with +8x%5E2%2B76x-34=0+
At this point I'm stuck on how to continue by using the quadratic equation.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A 10 by 14 meter garden will have a sidewalk of width x along the two 14 meter sides and width 2x along the two 10 meter sides. Approximate (to the nearest hundredths) the value of x that will make the area covered by sidewalks and the garden total 174 Square meters. (My teacher said to use the quadratic formula as well)
So I did (4x+10)(2x+14)=174 Ending up with +8x%5E2%2B76x-34=0+
At this point I'm stuck on how to continue by using the quadratic equation.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 8x%5E2%2B76x%2B-34+=+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=%2876%29%5E2-4%2A8%2A-34=6864.

Discriminant d=6864 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-76%2B-sqrt%28+6864+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2876%29%2Bsqrt%28+6864+%29%29%2F2%5C8+=+0.428078794301995
x%5B2%5D+=+%28-%2876%29-sqrt%28+6864+%29%29%2F2%5C8+=+-9.928078794302

Quadratic expression 8x%5E2%2B76x%2B-34 can be factored:
8x%5E2%2B76x%2B-34+=+%28x-0.428078794301995%29%2A%28x--9.928078794302%29
Again, the answer is: 0.428078794301995, -9.928078794302. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B76%2Ax%2B-34+%29

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