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

Apr 3, 2015

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

${x}^{2} - 4 x + 2 = 0$

Subtract the constant ($2$) from both sides
${x}^{2} - 4 x = - 2$

If ${x}^{2} + 4 x$ are the first two terms of a square of the form ${\left(x + a\right)}^{2}$
then
$a = - 2$ and the term needed to complete the square is ${a}^{2} = 4$

Add 4 to both sides of the equation
${x}^{2} - 4 x + 4 = 4 - 2$

Rewrite the left side as a square
${\left(x - 2\right)}^{2} = 2$

Take the square root of both sides
$x - 2 = \pm \sqrt{2}$

Giving the solutions
$x = 2 \pm \sqrt{2}$