$2 + 2 = 5$ (Fake proof, or ?) Basically, there is no error in the following steps(as it seems), but there is some error due to which 2 + 2 = 5. What is it?
                      -20 = -20
                    16-36 = 25-45
             16-36+(81/4) = 25-45+(81/4)
(4^2)-(2*4*9/2)+((9/2)^2) = (5^2)-(2*5*(9/2))+((9/2)^2)
              (4-(9/2))^2 = (5-(9/2))^2
                  4-(9/2) = 5-(9/2)
                        4 = 5
                      2+2 = 5


The problem is when you go from a quadratic to a linear.
$$(4-\frac{9}{2})^2 = (5-\frac{9}{2})^2$$
$$|4-\frac{9}{2}| = |5-\frac{9}{2}|$$
$$|\frac{-1}{2}| = |\frac{1}{2}|$$
$$\frac{1}{2} = \frac{1}{2}$$
