Completing the Square is the process of converting a quadratic equation into a perfect square trinomial by adding or subtracting terms on both sides.

Example of Completing the Square

x^{2} + 1 = 0 ⇒ (x + 1)^{2} = 2x In the example shown above, the term 2x is added on both sides to convert x^{2} + 1 = 0 into a perfect square trinomial.

Video Examples: Algebra - Completing the square

Solved Example on Completing the Square

Ques: Solve x^{2} + 10x = 39 by completing the square.

Choices:

A. - 13 and - 3
B. 1 and - 39
C. 13 and - 3
D. 3 and - 13
Correct Answer: D