Question

How do you solve by completing the square: `x^2 - 4x +2 = 0`?

Answer 1

(Please note that I edited your question to place a plus sign between the `4x` and the `2`; if you meant something else, perhaps a minus sign, please re-post).

`x^2-4x+2=0`

Subtract the constant (`2`) from both sides
`x^2-4x=-2`

If `x^2 +4x` are the first two terms of a square of the form `(x+a)^2`
then
`a=-2` and the term needed to complete the square is `a^2 =4`

Add 4 to both sides of the equation
`x^2-4x+4 = 4-2`

Rewrite the left side as a square
`(x-2)^2 = 2`

Take the square root of both sides
`x-2 = +-sqrt(2)`

Giving the solutions
`x = 2+-sqrt(2)`