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Completing the Square

Practise this technique for use in solving quadratic equations and analysing graphs.

Level 1 Level 2 Level 3 Level 4 Exam Style Description Help More Algebra

Solve the following quadratic equations by completing the square. Type in the two roots separated by a comma.

\(x^2 − 11x + 30 = 0\)

Correct Wrong

\(x^2 − 12x + 35 = 0\)

Correct Wrong

\(x^2 + 7x + 10 = 0\)

Correct Wrong

\(x^2 + 5x + 4 = 0\)

Correct Wrong

\(x^2 + 4x + 3 = 0\)

Correct Wrong

\(x^2 − 9x + 18 = 0\)

Correct Wrong

\(x^2 − 10x + 21 = 0\)

Correct Wrong

\(x^2 + 3x + 2 = 0\)

Correct Wrong

\(x^2 − 2x − 3 = 0\)

Correct Wrong


This is Completing the Square level 4. You can also try:
Level 1 Level 2 Level 3

Finally try some more quadratic equations that are a little more challenging.


Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

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Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

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Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.


If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Colleen Young, Twitter

Tuesday, December 6, 2016

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Description of Levels



Level 1 - Expressions with two terms such as \(x^2 + 6x\)

Level 2 - Expressions with three terms such as \(x^2 + 4x - 7\)

Level 3 - The coefficient of the squared term is greater than one such as \(2x^2 + 8x - 9\)

Level 4 - Use the ability to complete the square to help solve these basic quadratic equations

More Quadratic Equations - Use the ability to complete the square to help solve these more difficult quadratic equations.

Exam Style questions take the skill of completing the square and put it to use solving real problems. Typically problems involve solving equations or describing features of graphs. The questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Completing The Square

The video above is from the creative and aesthetically mindful Beth, a 3rd year Maths student at Oxford University.

Completing the square diagram

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up