Theorem: 4 = 5 'Proof': -20 = -20 (obviously...) 16 - 36 = 25 - 45 (just two different ways to write -20) 4^2 - 9*4 = 5^2 - 9*5 (factoring...) 4^2 - 9*4 + 81/4 = 5^2 - 9*5 + 81/4 (add 81/4 to both sides) (4 - 9/2)^2 = (5 - 9/2)^2 ("completing the square") 4 - 9/2 = 5 - 9/2 (get rid of the squares) 4 = 5 (cancel the 9/2 from both sides) 2+2=5 (proved)