由题意：x^2-2x+y^2+6y+10=0
即(x^2-2x+1)+(y^2+6y+9)=0
(x-1)^2+(y+3)^2=0
根据非负数的性质：x-1=0,y+3=0
即x=1,y=-3
故x+y=-2