Each side of a square is lengthened by 2 inches. the area of the new, larger square is 121 square inches. find the length of a side of the original square.

Let the original side length be x.  Then (x+2)^(in)^2 = 121 sq in.

Thus, x^2 + 4x + 4 = 121;
          x^2 + 4x - 117 = 0   =   (x-13)(x+9) = 0.  Then x = 13 and x = -9.

We need to discard the negative result (-9).

The side of the original square is 9 inches.            (answer)

Check:  does (9+2)^2 = 121?  Does 11^2 = 121?  YES.