- Mr Ausome

# O-Levels Math: How to Complete the Square Easily?

Completing the square of a quadratic equation is a very useful technique that is used for solving quadratic equations(E-Math), finding the turning point of a quadratic graph (E-Math) and finding the center of a circles equation (A-Math). However, students often forget the method and ask me frequently during our math tuition classes.

In this article, I will try to make the process of completing the square as simple and digestible as possible, but I will not further elaborate on the background reasoning behind it.

**Fundamental Step of Completing Square**

The key thing to completing the square is to remember this:

Formulas can be difficult to appreciate without the help of numbers.

**Observe the pattern** in the following examples of completing the square to understand the above formula:

To remember a formula, you have to practice!

**Completing the Square for a Typical Quadratic Equation**

After learning the core step in completing the square, we will have to apply it on a typical quadratic equation which has 3 terms. We complete the square the same way as the above section and we simply carry the x-independent term along.

**Observe the pattern** in the following examples of completing the square:

**Note that only the crucial step has been shown above. Please further simplify the equation by yourself.*

Time to test your understanding through practice!

**Completing the Square of more Complex Quadratic Equations**

In the previous parts, all the equations start with x^2. So how to we complete the square for equations where the x^2 has a different coefficient?

For example, how do we complete the square of

**Done!**

Now you have understood the art of completing the square! It is actually a very simple concept and yet students forget it again and again. Just make sure you remember the core formula above and you practice enough!

*"Don't practice until you get it right, practice until you can't get it wrong!" *

*~ Unknown*

To get professional help (Math tuition) on secondary school mathematics in Singapore, click here.

**Specialist Math Tutor**

**Mr Ausome**