How do I solve this problem?

Question

im having trouble on my Precalc homework. This is the problem: “a box is formed by removing squares of side length x inches from each corner of a rectangular piece of cardboard 10 inches wide by 16 inches long. Determine x so that the volume of the resulting box is 137.5 in3

im so confused

Answer 1

length of box = 10 - 2x

width of box = 16 - 2x

height of box = x

 

V = x(10 - 2x)(16 - 2x)

 

V = x(160 - 52x + 4x²)

 

V = 160x - 52x² + 4x³

 

Set this volume equal to 137.5.  This will result in the cubic equation

 

4x³ - 52x² + 160x - 137.5 = 0

 

 

You can use a graphing calculator to find the zeros.