Solve by completing the square x^2-4x-2=0?

x² - 4x + 4 = 2 + 4

[ x - 2 ]² = 6

x - 2 = ± √6

x = 2 ± √6

x² - 4x - 2 = 0

isolate the variables

x² - 4x = 2

coefficient of the x term: -4

divide in half: -2

square it: (-2)² = 2²

add 2² to both sides:

x² - 4x + 2² = 2 + 2²

(x-2)² = 6

x-2 = ±√6

x = 2±√6

x² - 4x - 2 = 0

x² - 2*2x + 2² - 2² - 2 = 0

(x - 2)² - 6 = 0

(x - 2)² - (√6)² = 0 [Factorize, a²-b² = (a+b)(a-b)]

(x - 2 + √6)(x - 2 - √6) = 0 [If ab=0 and a≠b then either a=0 or b=0]

Solutions: x = 2-√6 and x = 2+√6

Move the unit coefficient to the right (add 2 to both sides):

x² - 4x = 2

Complete the square:

a. Take the coefficient in front of x --> -4

b. Halve it --> -2

c. Square it --> (-2)² = 4

d. Add this to both sides:

x² - 4x + 4 = 6

The left side is a perfect square:

(x - 2)(x - 2) = 6

(x - 2)² = 6

Take the square root of both sides, remembering the ± sign:

x - 2 = ± √6

Add 2 to both sides to isolate x:

x = 2 ± √6

x^2 - 4x - 2 = 0

(x^2 - 4x) - 2 = 0

( x^2 - 4x + 4 - 4) - 2 = 0

(x^2 - 4x + 4) - 4 - 2 = 0

( x - 2)^2 = 6

x = 2 +/- sqrt(6)

= 2 + sqrt(6), 2 - sqrt(6)

(x-2)^2=srqt6

x-2=+-6

x=2+-6

thereforex=2+6 and x=2-6