Find the eccentricity of the ellipse

4x^2 + 16y^2 + 32x-32y+16=0

4x² + 16y² + 32x - 32y + 16 = 0

- 16 - 16

4x² + 16y² + 32x - 32y = - 16

4x² + 32x + 16y² - 32y = - 16

4 (x² + 8x + 16) + 16 (y² - 2y + 1) = - 16 + 4 (16) + 16 (1)

4 (x + 4) ² + 16 (y - 1) ² = - 16 + 64 + 16

4 (x + 4) ² + 16 (y - 1) ² = 48 + 16

4 (x + 4) ² + 16 (y - 1) ² = 64

64 64 64

(x + 4) ² + (y - 1) ² = 1

16 2