Question

Solve the following equation by using the method of completing the square:
$x^2-4x+1=0$

Answer 1

The difference of squares identity can be written:

$A^2-B^2=(A-B)(A+B)$

We can complete the square and use this with as follows:

$x^2-4x+10=0$

$x^2-4x+4-30=0$

$(x-2)2-\left(\sqrt{3}\right)20=0$

$\left(\right(x-2)-\sqrt{3})\left(\right(x-2)+\sqrt{3})=0$

$(x-2-\sqrt{3})(x-2+\sqrt{3})=0$

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