Question

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

The number that should be added to expression k^2+11 to make a perfect square is
(Simplify your answer. Type and integer or fraction)

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).