I need to know how to right the equation

Question

A box is to be made by cutting out the corners of a square piece of cardboard and folding the edges up. If 3 inch squares are to be cut out of the corners and the box contains 243 cubic inches, what is the length of side of the orginal cardboard square. The answer is 15 but I'm not understanding how to write the equation, can some one help me?

Answer 1

 

Well, then the height of the box is 3 inches.

 

If x is the length of one side of the square box, then

 the width of the box is x-6 and the length of the box

is x-6

 

Volume = length x width x height

 

243  =  (x-6) *(x-6) *3

 

3(x-6)^2 = 243

 

 (x-6)^2 = 81

 

 x^2 - 12x + 36 = 81

 

x^2 - 12x + 36 - 81 = 0

 

x^2 - 12x -  45 = 0

 

(x    -    15)(x   +        3 )  = 0

 

x +3 = 0 ---> x = -3 which results in a negative length

 

x-15 = 0 ---> x = 15