Question 60963
Let x = the width of the original piece of cardboard.  Then its length is x+2
If you were to cut out 2-unit squares from each corner and then fold up the flaps to create an open box, the width of the open box would be (x-4) and its length would be ((x+2)-4), and its height would, of course, be 2.
Now you can write the equation for the volume of the box as:
{{{V = (x-4)((x+2)-4)(2)}}} But the volume is given as 70 cubic units, so:
{{{(x-4)((x+2)-4)(2) = 70}}} Simplify and solve for x.
{{{(x-4)(x-2)(2) = 70}}}
{{{(x^2-6x+8)(2) = 70}}} Divide both sides by 2.
{{{x^2-6x+8 = 35}}} Subtract 35 from both sides.
{{{x^2-6x-27 = 0}}} Solve this quadratic equation for x by factoring.
{{{(x+3)(x-9) = 0}}} Applying the zero product principle, you get:
x = -3 Discard this solution as the width can't be a negative value.
x = 9 This is the width of the original piece of cardboard.
x+2 = 11 This is the length of the original piece of cardboard.

Check:

V = (9-4)(11-4)(2) = (5)(7)(2) = 70