Question 886368
x = side of square 1
2x+1 = side of square 2


difference in the areas is equal to 96 square inches.


that would be area of square 2 minus area of square 1 = 96


area of square 1 = x^2
area of square 2 = (2x+1)^2 = 4x^2 + 4x + 1


you get:


4x^2 + 4x + 1 - x^2 = 96


simplify to get:


3x^2 + 4x - 95 = 0


factor this to get:


(x-5) * (3x+19) = 0


solve for x to get:


x = 5 or x = -19/3


x can't be negative, so your solution can only be x = 5


replace x with 5 in the original equation to see if it holds true.


your original equation is:


x^2 = area of square 1
(2x+1)^2 = area of square 2
square 2 - square 1 = 96


replacing x with 5, we get:
area of square 1 = 25
area of square 2 = 121
square 2 - square 1 area = 121 - 25 = 96


x = 5 is your answer.