p2 – 12p + 32 = 0

(v) p² – 12p + 32 = 0

Sol. p² – 12p + 32 = 0

∴  p² – 12p = –32 .... (i)

Third term = ( ½ ×  coefficient of p)²

= ( ½ × - 12)²

= (– 6)²

= 36

Adding 36 to both sides of (i), we get,

p² – 12p + 36 = – 32 + 36

∴  (p – 6)² = 4

∴ p – 6 = ± √4

∴ p – 6 = ± 2

∴  p = 6 ± 2

∴  p = 6 + 2 or p = 6 – 2

∴ p = 8 or p = 4