-20 = -20 (obviously…)
=> 16 – 36 = 25 – 45 (just two different ways to write -20)
=> 42 – 9*4 = 52 – 9*5 (factoring…)
=> 42 – 9*4 + 81/4 = 52 – 9*5 + 81/4 (add 81/4 to both sides)
=> 42-2*4*9/2+(9/2)2 = 52-2*5*9/2+(9/2)2
(Only furnishes written)
=> (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)
=> 400 = 500 (multiplication with 100)
You tell your friend the mistake was….
4 – 9/2 = 8/2 – 9/2 = –1/2.
5 – 9/2 = 10/2 – 9/2 = 1/2.
You explain, Two different numbers can have the same square.
For example, (-3)^2 = 9 = 3^2, but -3 is not 3.
