An open box is made from a square piece of cardboard 30 inches wide by removing a square of side x from each corner and turning up the sides. Find the possible values of x if the box is to have a volume of 2000 cubic inches.

here you go IMG_0842.JPG

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so in the end where did the 5 or 20 come from? by factoring?

right, (30-2x)(30-2x)x=(30*30-30*2x*2+2x*2x)*x=2000

4x^3-120x^2+900x=2000

divide the whole thing by 4

x^3-30x^2+225x=500

x(x^2-30x+225)=500

x(x-15)^2=500

then you get the answer 5 and 20.

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