1) x²+y²+6x-10y+34=0
<=>(x²+2.3x+9)+(y²-2.5y+25)=0
<=>(x+3)²+(y-5)²=0
<=>$\left \{ {{(x+3)²=0} \atop {(y-5)²=0}} \right.$
<=>$\left \{ {{x+3=0} \atop {y-5=0}} \right.$
<=>$\left \{ {{x=-3} \atop {y=5}} \right.$
3) 9x²+12x+4y²+8y+8=0
<=>(9x²+2.3.2x+4)+(4y²+2.2.2y+4)=0
<=>(3x+2)²+(2y+2)²=0
<=>$\left \{ {{(3x+2²)=0} \atop {(2y+2)²=0}} \right.$
<=>$\left \{ {{3x+2=0} \atop {2y+2=0}} \right.$
<=>$\left \{ {{x=-2/3} \atop {y=-1}} \right.$
4) 4x²+9y²+20x-6y+26=0
<=>(4x²+2.2.5x+25)+(9y²-2.3y+1)=0
<=>(2x+5)²+(3y-1)²=0
<=>$\left \{ {{2x+5=0} \atop {3y-1=0}} \right.$
<=>$\left \{ {{x=-5/2} \atop {y=1/3}} \right.$
5) 3x²+3y²+6x-12y+15=0
<=>3(x²+2x+1)+3(y²-4y+4)=0
<=>3(x+1)²+3(y-2)²=0
<=>$\left \{ {{x+1=0} \atop {y-2=0}} \right.$
<=>$\left \{ {{x=-1} \atop {y=2}} \right.$
6) x²+4y²+4x-4y+5=0
<=>(x²+4x+4)+(4y²-4y+1)=0
<=>(x+2)²+(2y-1)²=0
<=>$\left \{ {{x+2=0} \atop {2y-1=0}} \right.$
<=>$\left \{ {{x=-2} \atop {y=1/2}} \right.$
