Question

Find the number that should be added to the expression to make a perfect square k^2+11k

Answer 1

k^2+11k has 11 as the coefficient of the first power of the variable (k).

To complete the square:

Take HALF of this coefficient.  In other words, take HALF of 11, obtaining 11/2.

Square this (11/2):  (121/4)

Add this 121/4   to  k^2+11k 

Result:     k^2+11k + 121/4

This is a perfect square:    k^2+11k + 121/4  = (k + 11/2)^2

Answer:  The number to be added to k^2 + 11k to make it a perfect square is  (121/4).