Does 2+2 really equal 5? there has been proof. but is it really correct?

I actually posted this a while ago and it got answerd by a smart person so here's what I understood

the error is that it assumes that √(x²)=x
because if x is negative, it becomes positive
that's how the 2nd line is wrong
the 2nd line is the first wrong step

it goes from 4-9/2+9/2
so it goes from 4-4.5+4.5
notice the part under the parenthsees
√((4-4.5)²)
if we evaluate 4-4.5, we get -0.5
but by squaring it we get 0.5

-0.5+4.5=4, yes
but when we square it we get
0.5+4.5=5, that is how it works

What are the options?