Объяснение:

[tex]x^2+y^2+4x-8y+20=0\\x^2+4x+y^2-8y+4+16=0\\(x^2+2*x*2+2^2)+(y^2-2*x*4+4^2)=0\\\left \{ {{(x+2)^2=0} \atop {(y-4)^2=0}} \right. \ \ \ \ \ \left \{ {{x+2=0} \atop {y-4=0}} \right. \ \ \ \ \ \left \{ {{x=-2} \atop {y=4}} \right. .[/tex]

Ответ: (-2;4).