Question

Solve the equation by completing the square 2x^2 - 4x + 5 = 6

Answer 1

The equation 2x^2 - 4x + 5 = 6

Separate variables and constants aside by subtracting 5 to each side.

2x^2 - 4x   =   1

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

x^2 - 2x   =   1/2

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

x^2 - 2x + 1   =   1/2 + 1

(x - 1)^2   =   (1 + 2)/2

(x - 1)^2   =   3/2

Take square root on both sides.

(x - 1)   =   ± √(3/2)

x   =  1  ± √(3/2)

Solutions are x = 1 + √(3/2) and x = 1 - √(3/2)