Add us as your Algebra Help Resource!

Completing the square


Completing the square requires relatively basic manipulation of quadratic equations. Students must first realise that

equation that shows how completing of squares is used

Every quadration equation of the form can be written as constant . This procedure generally takes 4 steps. Let us go through on how to proceed with completing the squares.

1. Express as

2. Then , we modify the expression inside the brackets so that it will fit into the form procedure on how to complete the square of a quadratic function.

To do so , we add (which is the square of the 'a' coefficient in the x term above) within the brackets. To ensure that the equation stays balanced, we have to subtract outside of the brackets.

Thus , the equation will look something like this :

= answer to the completing the square question

We write it as 2( ) x to clearly state the specific coefficients.

3. We would then be able to simplify the expression to .

Finally , we have managed to complete the squares.


Although these 3 steps to completing the square may seem complicated, let us try some examples to clarify our understanding.

a) Complete the squares for

First, we would take out the 3 and we would obtain From there, we attempt to turn the expression within the brackets into a square. In this example, we have to add 1/9 (square of 1/3) within the brackets. After multiplying with the 3 outside, we realize that we have to deduct 1/3 outside in order to balance the equation.



Thus, we have managed to complete the squares.

'Try it Yourself' Section

Try completing the squares with the below exercises. Practise is crucial if you wish to be good at completing the squares.

a) completing the square question


If you would like to share this article, feel free to syndicate it with a link to this article or to our algebra help site ,stating its ownership .Legal action will be taken against those who do not do so.For more information on linking, please go to 'link to us' link found below.