Question 136353
Given: {{{x^2-3x+1=0}}}

to complete the square, use this format
(ax^2 + 2abx + b^2)
We are given
{{{x^2-3x+1=0}}}  , so a = 1 and 2ab=-3 --> b = -3/2 --> b^2 = 9/4


{{{x^2-3x + 9/4  +1= (9/4)}}} whatever you do to one side, you need to do to the other

{{{(x- 1.5)^2 = (9/4) - 1 }}}
{{{ (x-1.5)^2 = 5/4 }}}
{{{ (x-1.5) = sqrt(5/4)}}}
{{{x = sqrt(5/4) + 1.5 }}}
{{{x = 1.5 + sqrt(5)/2}}}
{{{x = 1.5 - sqrt(5)/2}}}