Question

Solve the following equation by completing the square 6x2-6x-1-0 To complete the square,

Answer 1

The equation 6x^2 - 6x - 1  =  0

Separate variables and constants aside by add 1 to each side.

6x^2 - 6x  =  1

Here x^2 coefficient is 6 , for perfect square make x^2 coefficient 1 by dividing each side by 6.

x^2 - x   =   1/6

To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

x^2 - x + (1/2)^2   =   1/6 + (1/2)^2

(x - 1/2)^2   =   1/6 + 1/4

(x - 1/2)^2   =   (2 + 3) / 12

(x - 1/2)^2   =   5 / 12

Take square root on both sides.

(x - 1/2)   =   ± √(5/12)

x   =  1/2  ± √(5/12)

Solutions are x = 1/2  + √(5/12) and x = 1/2  - √(5/12)

Answer :

Solutions are x = 1/2  + √(5/12) and x = 1/2  - √(5/12)