Maximizing Volume Formula for Given Box Dimensions and Cut Size

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Homework Statement


A box is given with a L = 1.414w and W = w and a cut size = x. Find the general formula for the maximum volume.

Homework Equations


L = 1.414w - 2x
W = w - 2x
H = x

The Attempt at a Solution


V = x(1.414w - 2x)(w - 2x)
V = 4x3 - 4.818x2w + 1.414w2
Apparently this isn't the general formula for max volume, so someone please help.
 
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Never mind guys. I figured it out.
 
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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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