x^2+xy-2y^2+3x+3y+2
=(x+2y)(x-y)+(x+2y)+2x+y+2
=(x+2y)(x-y+1)+x-y+1+x+2y+1
=(x+2y+1)(x-y+1)+x+2y+1
=(x+2y+1)(x-y+2)
x+2y+1=0
所以
x^2+xy-2y^2+3x+3y+2=0