Question 738317

{{{36x^2-4y^2+216x-40y+80=0}}}

 first  complete the square :

{{{36x^2-4y^2+216x-40y+80 = 0}}}...group like terms

{{{(36x^2+216x)-(4y^2+40y)+80 = 0}}}...factor

{{{36(x^2+6x)-4(y^2+10y)+80 = 0}}}.....complete the square 

{{{36(x^2 + 6x + ____) - 4(y^2 + 10y + ____) = -80}}}

{{{36(x^2 + 6x + 9) -324- 4(y^2 +10y + 25)-(-4*25) = -80}}}

{{{36(x^2 + 6x + 9) -324- 4(y^2 +10y + 25)+100 = -80}}}

{{{36(x^2 + 6x + 9) - 4(y^2 +10y + 25) = -80+324-100}}}

{{{36(x^2 + 6x + 9) - 4(y^2 +10y + 25) = 144}}}

{{{36 (x+3)^2-4 (y+5)^2-144=0}}}