COMPLETING THE SQUARE

Completing The Square

Definition Of Completing The Square

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

x² + 1 = 0 ⇒ (x + 1)² = 2x In the example shown above, the term 2x is added on both sides to convert x² + 1 = 0 into a perfect square trinomial.

Video Examples: Algebra - Completing the square

Solved Example on Completing the Square

Ques: Solve x² + 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

Solution:

Step 1: x² + 10x = 39 ⇒ x² + 10x + 25 = 39 + 25
Step 2: (x + 5)² = 64 ⇒ x + 5 = - 8 or 8
Step 3: x = 3 or - 13

Quick Summary

Transform a quadratic equation into vertex form.
Useful for solving quadratic equations and graphing parabolas.

\[ (x + a)^2 = x^2 + 2ax + a^2 \]

🍎 Teacher Insights

Emphasize the visual representation of completing the square with geometric models.

🎓 Prerequisites

Basic Algebra
Quadratic Equations
Factoring

Check Your Knowledge

Q1: Solve x^2 + 10x = 39 by completing the square.

-13 and -3 1 and -39 13 and -3 3 and -13

Frequently Asked Questions

Q: Why do we complete the square?
A: To rewrite the quadratic equation in a form that reveals the vertex of the parabola and allows for easier solving.

Q: What if the coefficient of x^2 is not 1?
A: Divide the entire equation by the coefficient of x^2 before completing the square.