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

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Answer 1 · 2016-03-20T00:21:35

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

$a^2-b^2 = (a-b)(a+b)$

with $a=(x-2)$ and $b=sqrt(3)$ as follows:

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

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

$=(x-2)^2-(sqrt(3))^2$

$=((x-2)-sqrt(3))((x-2)+sqrt(3))$

$=(x-2-sqrt(3))(x-2+sqrt(3))$

So: $x=2+-sqrt(3)$

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