Solve the equation by completing the square Enter answer as

Solution

Given that

x² = 6x - 6

Solving by completing the square

x² - 6x = - 6

Adding 9 on both sides

x² - 6x + 9 = - 6 + 9

x² - 6x + (3)² = 3

x² - 2.3.x + (3)² = 3

( x - 3 )² = 3 [since , a² - 2ab + b² = (a - b)² ]

For f²(x) = f(a) , the solutions are f(a) and  - f(a)

( x - 3 ) = 3 , ( x - 3 ) = -3

x = 3 + 3 , x = - 3 + 3

x = 4.73205 , x = 1.26795

Therefore,

x = 4.73205 , 1.26795