What's wrong with this proof??

[Syringer]

-20 = -20
16 - 36 = 25 - 45
4^2 - 9*4 = 5^2 - 9*5
4^2 - 9*4 + 81/4 = 5^2 - 9*5 + 81/4
(4 - 9/2)^2 = (5 - 9/2)^2
4 - 9/2 = 5 - 9/2
4 = 5

I imagine it has to do with the 5th step, where they factor that expression..but I don't see anything wrong with their method..as (a-b)^2 does in fact equal a^2 + 2ab + b^2..where's the error?

 

[aux]

x^2 = y ^2 does not imply x = y, it implies |x| = |y|
|x| being the absolute value of x

(4 - 9/2)^2 = (5 - 9/2)^2 is ok, but the next line should be
|4 - 9/2| = |5 - 9/2| or
| -0.5| = |0.5| which is just fine

 

[Syringer]

Ah, thanks