On a Square with Side Lengths and Area = to 1

Way over my head. I'm just not very good at doing math. Basically, I just did a system of equation, and got this answer "y^2-1/2y+1=0". Not sure if that's a solution.

2x+2y=x*y

And then 2x+2y=1

And then

x=1/2-y

And then 2(1/2-y) + 2y =(1/2-y)*y

And then 1-2y+2y = 1/2y-y^2

And then 1=1/2y-y^2

And then -y^2 +1/2y-1=0

And then y^2-1/2y+1=0

Someone explain to me what I did wrong, if anything.

But it's not possible because it's an imaginary number or negative. You'd have to work in other dimensions to make a square like that, or work in negatives, so nothing in physical space can accomplish that.