Question 923984
{{{x^2-3x+(3/2)^2-(3/2)^2+1=0}}}, for completing the square;
{{{(x-3/2)^2=(3/2)^2-1}}}
{{{(x-3/2)^2=9/4-4/4}}}
{{{(x-3/2)^2=5/4}}}
{{{x-3/2=0+- (1/2)sqrt(5)}}}
{{{x=3/2+- (1/2)sqrt(5)}}}


Look again at the original quadratic equation.  
{{{x^2+1=3x}}}, and you already see the solution obtained for x.


{{{highlight(x^2+1=9/2+- (3/2)sqrt(5))}}}