Completing the square

This is a very old-school and technical method we learnt in secondary school. However, many students are unable to do it accurately still. The trick of completing the square is realising that it depends on our (even older) $(a\pm b)^2=a^2 \pm 2ab + b^2$ formula. We are always introducing the $-b^2$ after we complete the square to ensure the expression is kept the same.

square

Students should know the completing the square is a technique, not confined to just quadratic expressions.

For example,
$5-4\sqrt{x}+x=(\sqrt{x}-2)^2 +1$

About

KS Teng

KS has been teaching H2/H1 Mathematics and IB mathematics for the more than 10 years. Having taught students from all various Junior Colleges, KS adapts to students' abilities and help them better understand the topics. As someone who loves to teach mathematics and sees it as a truly useful tool in life, KS seeks to enable students to appreciate math. Therefore, his tuition mission is to motivate and cultivate students to be independent and confident thinkers.

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Completing the square

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