Question

Solve, by completing the square, x^2=22x-5, leave your answer in surd form

Answer 1

a) The complete square form = ( x-11)² = 116

b) x = 11 + 2√29

Explanation:

Step(i):-

Given equation x² = 22x -5

⇒ x² - 22x + 5 =0

⇒ x² - 2× 11 x + (11)² -(11)² + 5=0

⇒ ( x- 11)² -121 +5 =0

⇒ ( x-11)² = 116

The complete square form = ( x-11)² = 116

Step(ii):-

⇒ (x-11) = √116 = √29 ×√4

⇒ x-11 = 2√29

⇒ x = 11 + 2√29