SOLUTION: Please help! I need assistance with this college level challenge problem! I worked out the problem but sadly, to no avail. Link to the problem: https://www.scribd.com/document/3

Question 1055963: Please help! I need assistance with this college level challenge problem! I worked out the problem but sadly, to no avail.
Link to the problem: https://www.scribd.com/document/329683850/Challenge-Problem-3
Any help would be much appreciated thank you!

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Please help! I need assistance with this college level challenge problem! I worked out the problem but sadly, to no avail.
Link to the problem: https://www.scribd.com/document/329683850/Challenge-
===============
You want to make an 80 cubic inch out of a 10 by 12 inch sheet. Why not just say that? Are you a drama major?
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Cut squares of size x by x from each corner.
Vol = x*(12-2x)*(10-2x) = 80
4x^3 - 44x^2 + 120x - 80 = 0
--------
x^3 - 11x^2 + 30x - 20 = 0
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Try factors of 20 first, 1, 2, 4, 5, 10 & 20
f(x) = x^3 - 11x^2 + 30x - 20
f(1) = 0 --> x-1 is a factor.
Divide by x-1
------
--> g(x) = x^2 - 10x + 20

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=20 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 7.23606797749979, 2.76393202250021. Here's your graph:

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