Question

solve the quadratic equation by method of completing perfect square.

x²-10x+16=0

Answer 1

Given : x² - 10x + 16 = 0

⇒ x² - 2 × x × 5 + 16 = 0

⇒ x² - 2 × x × 5 + 16 + 5² - 5² = 0

⇒ x² - 2 × x × 5 + 5² + 16 - 25 = 0

⇒ (x - 5)² - 9 = 0

⇒ (x - 5)² = 9

⇒ (x - 5) = √9 = ±3

⇒ x = 5 ± 3 = 5 + 3 or 5 - 3 = 8 or 2