Complete the square of X^2+Y^2+2X+2Y=1

I got

Y=+/- sqrt[2-(x+1)^2]-1

Because I added 1 to the right side of the equation twice.

Where did I go wrong?

Thanks.

x^2 + y^2 + 2x + 2y = 1

(x^2 + 2x) + (y^2 + 2y) = 1

complete square for x terms

(b/2a)^2 = (2/((2)(1))^2 = (2/2)^2 = 1^1 = 1

complete square for y terms

(b/2a)^2 = (2/((2)(1))^2 = (2/2)^2 = 1^1 = 1

add 2 to both sides of the equation and we get

(x^2 + 2x + 1) + (y^2 + 2y + 1) = 1 + 2

(x + 1)^2 + (y + 1)^2 = 3

this is an equation of circle with center at (- 1, - 1) and radius of sqrt(3)