What must you add to the expression x2+bxx2+bx to complete the square?

We are given the incomplete expression:

x^2 + b x

Now to complete the square, we need to add the square of the half of b, that is:

(b / 2)^2

or

b^2 / 4

Therefore the complete expression is:

x^2 + b x + (b^2 / 4)