Question

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

Answer 1

Answer:

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

b)   x = 11 + 2√29

Step-by-step 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