SOLUTION: Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base

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Question 175009: Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be 80 square inches, then what size square should be cut from each corner?
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
2. Thomas is going to make an open-top box by cutting equal squares
from the 4 corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides.
If the area of the base is to be 80 square inches,
then what size square should be cut from each corner?"
Let x = side of the cut-out squares.
The length of the base is: 14 - 2x inches.
The width of the base is: 11 - 2x inches.
The area of the base is 80 in².
There is our equation: (14 - 2x)(11 - 2x) = 80
and we have the quadratic: 2x² - 25x + 37 = 0
:
highlight%28x=1.72%29 in.
:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-25x%2B37+=+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=%28-25%29%5E2-4%2A2%2A37=329.

Discriminant d=329 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--25%2B-sqrt%28+329+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-25%29%2Bsqrt%28+329+%29%29%2F2%5C2+=+10.7845892868043
x%5B2%5D+=+%28-%28-25%29-sqrt%28+329+%29%29%2F2%5C2+=+1.71541071319574

Quadratic expression 2x%5E2%2B-25x%2B37 can be factored:
2x%5E2%2B-25x%2B37+=+%28x-10.7845892868043%29%2A%28x-1.71541071319574%29
Again, the answer is: 10.7845892868043, 1.71541071319574. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-25%2Ax%2B37+%29