Question 1086031


{{{x^2-x-1=0}}}.....to complete square, recall {{{(a-b)^2=a^2-2ab+b^2}}};so, we need to add and subtract {{{b^2}}} 

{{{(x^2-x+b^2)-b^2-1=0}}}.. ..since coefficients {{{a=1}}}and {{{2ab=-1}}}, we have {{{2*1*b=-1}}}->{{{2b=-1}}}->{{{b=-1/2}}}

{{{(x^2-x+(-1/2)^2)-(-1/2)^2-1=0}}}

{{{(x-1/2)^2-(1/4)-1=0}}}

{{{(x-1/2)^2-1/4-4/4=0}}}

{{{(x-1/2)^2-5/4=0}}}

{{{(x-1/2)^2=5/4}}}