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Completing the square rewrites a quadratic as (x + p)² + q, revealing the turning point and giving another way to solve quadratic equations. It's examined right across GCSE and iGCSE Maths. Work through it free on eClassroom, with clear worked examples and instantly-marked questions that build your confidence for the exam.
How you do it
Halve the coefficient of x and put it inside the bracket, then subtract the square of that number to correct the overshoot. The result gives the turning point directly and lets you solve by taking the square root of both sides.
Before you start
You need expanding and factorising before this makes sense. It carries straight through to turning points and the quadratic formula. Assessed at Higher tier.
What you learn
Completing the square rewrites x² + bx + c in the form (x + p)² + q. Once in the form (x + p)² + q = 0, rearrange to (x + p)² = −q, take the square root of both sides (remember ±), then solve for x. In completed-square form (x + p)² + q, the smallest value is q (since a square is never negative), and it happens when x = −p. The course works through completing the square, solving by completing the square and the minimum point. Every section has instant-feedback practice questions matched to Edexcel iGCSE 4MA1 and the other major GCSE boards, and the course finishes with full exam-style questions you mark yourself.
Related Topics
In our GCSE maths courses, Completing the Square belongs to Algebra and is met in Higher tier. There are 3 teaching sections and 2 fully worked examples, plus 3 sets of check questions. Related topics students usually take next include Differentiation, Expanding Brackets and Factorising. You can drill this strand further on the Algebra revision engine, with your accuracy saved to your skill tree.
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