Here's your text with improved grammar and unnecessary words removed: Assume you need to create an open box from a square cardboard sheet by cutting out equal squares from each corner and folding along the dotted lines. The box's volume is 972 cubic inches. Determine the box's length and width, formulate the equation for the volume, then solve the equation to find the box's dimensions.

To create an open box from a square cardboard sheet by cutting out equal squares from each corner, you'll start with a square piece of cardboard with side lengths we'll call 's'. The sides of the squares being cut out we'll call 'x'.

Here are the steps to follow:

1. Draw a square and represent the cuts: Imagine a square cardboard; label its sides 's' and the squares being cut out of each corner 'x'.

2. Derive the formula: Once the corners are cut out and the sides are folded up, the length of the box will be 's - 2x', the width will also be 's - 2x', and the height will be 'x'. The volume of the box (V) can be calculated as the product of length, width, and height: V = (s - 2x)(s - 2x)x.

3. Solve for 's', given the volume: You're given that the volume is 972 cubic inches, so this becomes:

972 = (s - 2x)(s - 2x)x.

To find the box's dimensions, you need to solve this cubic equation for 'x', keeping in mind that 's - 2x' would give you the length and width.

Unfortunately, this is not possible to do with the information provided. The reason is that we have a cubic equation with two unknowns ('s' and 'x'). Typically, there's a given dimension for 's' or a relationship between 's' and 'x' is provided. Without this additional piece of information, the problem has infinite solutions as there are multiple combinations of 's' and 'x' that can yield a volume of 972 cubic inches.