x2 + 8x + 9 = 0

(i) x² + 8x + 9 = 0

Sol. x² + 8x + 9 = 0

∴  x2 + 8x = –9 .....(i)

Third term = ( ½ ×  coefficient of x)²

= ( ½ × 8)²

= (4)²

= 16

Adding 16 to both sides of (i) we get,

x² + 8x + 16 = –9 + 16

∴  (x + 4)² = 7

∴  (x + 4) = ±√7

∴  x = – 4 ±√7

∴ x = – 4 +√7  or x = – 4 – √7