Example 2
x^{2} + 2x + 5 = (x + 2/2)^{2} - (2/2) ^{2} + 5 = (x + 1)^{2} - 1 + 5 = (x + 1)^{2} + 4
When completing the square when the leading coefficient is not equal to 1, we factor out the leading coefficient and work inside the brackets.

Exercise:Complete the square for the following quadratic expressions

(answers given below)

Exercises

Complete the square for the following quadratic expressions (answers given below)
A) x^{2} + 4x
B) x^{2} + 6x - 3
C) -x^{2} - 4x + 2
D) -2x^{2} - 5x - 5