A wire of length 20 is cut in two pieces. One piece is made into a square, and the other piece is made into a rectangle that is 3 times as long as it is wide. Find f(x) = the sum of the areas of the two shapes, where x is the short side of the 1:3 rectangle.
Your answer should be f(x) = Ax² + Bx + C for some numbers A, B, C. What is A+B+C?