16x^2+4y^2-32x+16y-32=0
16x^2 - 32x + 4y^2 + 16y = 32
look at the x's first, divide by 16
x^2 - 2x + 1 complete the square
take half of -2, -1 now square it +1
(x - 1)^2 is first part
(x -1)^2 + 4y^2 + 16y = 32 + 1
add the 1 to both sides
4y^2 + 16y
y^2 + 4y divide by 4
complete the square
y^2 + 4y + 4
(y+2)^2
(x - 1)^2 + (y + 2) ^2 = 33 + 4
(x - 1)^2 + (y + 2) ^2 = 37