x^2+2x+y^2+6y+10＝0
x^2+2x+1+y^2+6y+9＝0
(x+1)^2+(y+3)^2＝0
(x+1)^2=0,(y+3)^2＝0
x=-1,y=-3
x+y=-1-3=-4