# How do you solve using the completing the square method x^2-4x+1=0?

Mar 20, 2016

See explanation...

#### Explanation:

In addition to completing the square, I will use the difference of squares identity, which can be written:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

with $a = \left(x - 2\right)$ and $b = \sqrt{3}$ as follows:

$0 = {x}^{2} - 4 x + 1$

$= {x}^{2} - 4 x + 4 - 3$

$= {\left(x - 2\right)}^{2} - {\left(\sqrt{3}\right)}^{2}$

$= \left(\left(x - 2\right) - \sqrt{3}\right) \left(\left(x - 2\right) + \sqrt{3}\right)$

$= \left(x - 2 - \sqrt{3}\right) \left(x - 2 + \sqrt{3}\right)$

So: $x = 2 \pm \sqrt{3}$