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What you need to know
What you need to know:
Completing the square involves manipulating a quadratic equation to put it into a different algebraic form. You should be able to complete the square on any quadratic that you are asked to, and then use this new form to help you solve the equation (if required). Note, you will not be asked to complete the square on a quadratic that has no x term. For example, it doesn’t make sense to discuss completing the square of x^2 - 16, so you won’t be asked to do it.
If you were to complete the square on the quadratic x^2 + 6x + 8, then in two steps you would get:
x^2 + 6x + 8 = (x + 3)^2 - 9 + 8 = (x + 3)^2 - 1
So the final result of completing the square is (x + 3)^2 + 1. Thus, the problem of quadratic equation x^2 + 6x + 8 = 0 becomes the problem of solving (x + 3)^2 - 1 = 0. If, at this point, we add 1 to both sides (in this example, the number will differ of course) and then square root both sides, it becomes obvious how this can quickly present us with the solutions to the quadratic equation.
Completing the Square Revision and Worksheets
Completing the square revision materials and resources can be accessed via this page. You may be a York Maths Tutor or you may be a maths teacher in London, wherever you are, whether you are teaching or tutoring Maths, the completing he square resources will be a useful addition to your bank of GCSE Maths questions that you use with your pupils.
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