Question 399145
For {{{x^2 + bx + c}}}, you divide b by 2, square the result to get {{{b^2/4}}}, and add AND subtract {{{b^2/4}}}  to retain the original expression.

Hence {{{x^2 + bx + c = x^2 + bx  +b^2/4 + c - b^2/4 = (x + b/2)^2 + (4c - b^2)/4}}}