Complete the square
- Half the coefficient of x.
- Put it in a bracket squared.
- Adjust the constant if needed.
Answer: x² + 8x + 16 = (x + 4)²
𝑥 Algebra
Completing the square
Learn completing the square with a GCSE-style explanation, help guide, worked example, practice question and flashcards.
Global XP
Level 10 / 100 XP
1. Explanation
Key idea
- Completing the square is part of advanced topics and appears often in KS3–GCSE maths.
- Completing the square rewrites a quadratic in bracket-square form.
- Use the worked model, help guide, interactive question and flashcards to practise completing the square until the steps feel automatic.
Real-life examples
- Shopping, sport, travel, science, design and everyday decisions all use this skill.
2. Visual
Completing the square learning map
Understand the key idea → follow the help guide → practise a question → check your method → build speed with flashcards.
3. Help guide
How to tackle Completing the square
- Learn the rule: Completing the square rewrites a quadratic in bracket-square form.
- Worked model: Half the coefficient of x. Put it in a bracket squared. Adjust the constant if needed.
- Try the interactive question without looking at the answer first.
- Use the flashcards to test the rule, the method and a common check.
4. Worked examples
Step-by-step working
5. Interactive questions
Try it yourself
Complete the square: x² + 6x + 9.
6. Flashcards
Master quick recall
Flip each card, then choose whether you know it or need more practice.
0 mastered
FrontRule for Completing the square
BackCompleting the square rewrites a quadratic in bracket-square form.
FrontExample answer: Complete the square: x² + 6x + 9.
Backx² + 6x + 9 = (x + 3)².
FrontCommon check for Completing the square
BackCheck units/notation, compare with an estimate, and make sure the answer matches the question.
7. Finish
Complete this topic
When you have read the examples, tried the question and reviewed flashcards, claim your topic completion XP.