Completing the square
Completing the square means rewriting a quadratic expression so that part of it becomes a perfect square trinomial.
Practice This ConceptMain explanation
Teacher explanation
This method is useful when factorisation is not easy. By adding and subtracting the right value, the quadratic can be written in a form that is easier to solve or analyse.
Example
x^2 + 6x + 5 can be written as (x + 3)^2 - 4.
Simple analogy
Half the x term, then square it.
Common confusion
Students often add half of b instead of adding the square of half of b.
Exam tip
For x^2 + bx, add (b/2)^2 to complete the square, then keep the equation balanced.
Answer writing and exam use
1-mark use
Write the exact meaning of completing the square in one clean line.
2-mark use
Define completing the square and add one example or condition.
3-mark use
Explain completing the square, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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