Weird differential equation Keep getting it wrong

dx/dt= (2-x) (1-x)

Found out from a previous question that the integral of 1/(2-x)(1-x) is

ln |(2-x)/(1-x)| +c

Right so

I separate the variables and intergrate and thus obtain

ln |(2-x)/(1-x)| +c = t

Additionally, when t=0, x=0

so therefore c=0

Now here comes the interesting part.. what is x when t=0.5

The answer is 0.56 (2.s.f.)

So I obtain e^0.5(1-x)= 2-x

e^0.5 - x (e^0.5) =2-x

e^0.5= 2-x+xe^0.5
e^0.5-2= xe^0.5-x

therefore x= e^0.5-2/ (e^0.5-1)

AND MY ANSWER IS FRICKIN WRNONG?!!!?!