Question 249038
Let x = length of the original square

So (x+8)^2=289

Take the square root of each side of the equation.  

So x+8 = 17 and -17

Solve each linear equation

x+8=17, so x=9

and x+8=-17, so x = -25.

Since I believe that the question is dealing with a real, physical square, the second answer (x=-25) is dropped and the answer is x=9 cm.

Good luck with your math studies.