We need to complete the square for the x and x^2 terms and then for the y and y^2 terms.
First, reorder the terms
-9x^2+72x+4y^2-16y=164
Factor out a -9 from the first 2 terms.
*Remember to change the signs.
Factor out a 4 from the last 2 terms.
-9(x^2-8x)+4(y^2-4y)=164
Work with the x term.
(-8/2)^2=(-4)^2=16
Remember that we factor out -9 so, we have to add -9*4=-36 to the right side of the equation.
Work with the y term.
(-4/2)^2=(-2)^2=4
Remember that we factor out 4 so, we have to add 4*4=16 to the right side of the equation.
-9(x^2-8x+16)+4(y^2-4y+4)=164-144+16
Factor:
x^2-8x+16=>(x-4)^2 => Perfect square trinomial
y^2-4y+4=>(y-2)^2 => Perfect square trinomial
-9(x-4)^2+4(y-2)^2=164-144+16
-9(x-4)^2+4(y-2)^2=36
(-9(x-4)^2)/36+(4(y-2)^2)/36=36/36
-((x-4)^2)/4+((y-2)^2)/9=1
