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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.

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In this article, I will tryÂ 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.

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Fundamental Step of Completing Square

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

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

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

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ToÂ remember a formula, you have to practice!

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Completing the Square for a Typical Quadratic Equation

After learning the core step in completing the square, we will have to apply it on aÂ 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.

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

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

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Time to test your understanding through practice!

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Completing the Square of more Complex Quadratic Equations

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

For example, how do we complete the square of

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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!

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

~ Unknown

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

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Mr Ausome

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