Solving a quadratic equation by completing the square

Question

Solve the quadratic equation by completing the square. x^2-12x +22=0

Answer 1

The equation x^2 - 12x +  22  =  0

Separate variables and constants aside by subtracting 22 to each side.

x^2 - 12x +  22 - 22  =  0 - 22

x^2 - 12x  =  -22

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

x^2 - 12x + (6)^2   =   -22 + 6^2

x^2 - 12x + (6)^2   =   -22 + 36

(x - 6)^2   =   14

Take square root on both sides.

(x - 6)   =   ± √14

x   =  6  ± √14

Solutions are x = 6  + √14 and x = 6  - √14

Answer :

Solutions are x = 6  + √14 and x = 6  - √14