#Integration Using Completing the Square

#Table of Contents

1. What is Completing the Square?
2. Integrating Using Completing the Square
3. Worked Example
4. Practice Questions
5. Glossary
6. Summary and Key Takeaways

#What is Completing the Square?

#Introduction

Completing the square is a method used to rewrite quadratic expressions in a way that makes them easier to manipulate, particularly for solving equations and integrating.

#Quadratic Expression

A quadratic expression is of the form: $$a{x}^{2} + bx + c$$

#Simple Version of Completing the Square

For a quadratic expression without a leading coefficient: $${x}^{2} + bx + c = \left(x + \frac{b}{2}\right)^{2} + c - \left(\frac{b}{2}\right)^{2}$$

#Completing the Square with a Leading Coefficient

When a coefficient is in front of the $x^{2}$ term: $$a{x}^{2} + bx + c = a\left(x + \frac{b}{2a}\right)^{2} + c - a\left(\frac{b}{2a}\right)^{2}$$