Question 775715
{{{x^2 + x}}}
= {{{x^2 + 2*x*(1/2)}}}


If {{{(1/2)^2}}} is added then the expression becomes
= {{{x^2 + 2*x*(1/2) + (1/2)^2}}}
= {{{(x+1/2)^2}}}


Hence, to convert the given expression into a perfect square {{{1/4}}} needs to be added.