A box with a square base and no top is to be made from a square piece of carboard by cutting 7 in. squares from each corner and folding up the sides. The box is to hold 16128 in3. How big a piece of cardboard is needed?

?in by ?in

2 answers

base area = (w-14)(w-14)
h = 7
volume = 7 (w-14)^2 = 16128

w^2-28w+196 = 2304

w^2 - 28 w - 2108 = 0

(w-62)(w+34) = 0

w = 62
side of base = x-14
height = 7

solve
7(x-14)^2 = 16128
(x-14)^2 = 2304

I will let you finish it.