00:01
In this question, we're given that the volume of the box is 504 cubic inches.
00:09
We're going to be finding the value of x in inches, assuming that all dimensions in the figure are in inches.
00:17
Now the volume of this box is given by the formula, length times width times height.
00:24
So we can do the substitutions.
00:26
So the volume is 504, the length is x plus 2, the width is x and the height is 8.
00:41
Now let's open up the bracket.
00:44
We have x times x, that's going to be x squared, plus 2x, and also we multiply by 8 to get 504.
00:58
Now what we could do from here is just divide both sides by 8 and that will lead to 63 equals x squared plus 2x.
01:11
We then form a quadratic equation x squared plus 2x minus 63 equals 0.
01:20
We need to find a pair of numbers whose sum is 2 and the product is negative 63.
01:31
And the numbers, the pair, is 7 and 9.
01:37
And so then the value that takes a negative value or the negative sign is 7...