The square root of a^2 has 2 solutions : +a and -a.

So, when you take the square root of the 2 members of an identity, you should connect the solutions properly to still have an identity.

In fact, 4 - 9/2 = - (5 - 9/2)
4 - 4.5 = - (5 - 4.5)
- 0.5 = - (0.5)
- 0.5 = - 0.5 is correct.

Nice try,

Jean-Marie