Question 83341
{{{x^2+2x+y^2+6y+6=0}}} Start with the given equation


{{{x^2+2x+y^2+6y=-6}}} Subtract 6 from both sides


{{{(x^2+2x)+(y^2+6y)=-6}}} Group like terms


{{{(x^2+2x+2)+(y^2+6y+9)=-6+2+9}}} Complete the square


{{{(x^2+2x+2)+(y^2+6y+9)=5}}} Add


{{{(x+1)^2+(y+3)^2=5}}} Factor


So the equation is a circle with a radius of {{{sqrt(5)}}} and a center of (-1,-3)