Aladder of length 2x+1 feet is positioned against a wall such that bottom is x-1 feet away from a wall. the distance between the floor and top of the ladder is 2x. assume that a right angle is formed by wall and the floor.

Pythagorean theorem
c^2 = a^2 + b^2

c = 2x+1
a = 2x
b = x-1

plug in and get:
(2x+1)^2 = (2x)^2 + (x-1)^2
4x^2 + 4x + 1 = 4x^2 + x^2 - 2x + 1    [distributed]
4x^2 + 4x + 1 = 5x^2 - 2x + 1    [added like terms]
x^2 - 6x = 0   [subtracted 4x^2 and 4x and 1]
x(x-6)=0     [factored out x]
x can equal 0 or 6

0 would not make any sense physically
therefore x = 6
plug this back into the length of the ladder 2x+1
2(6)+1 = 12 + 1 = 13

therefore the ladder is 13 feet long