Mathematics · Grades 9–12
Complete the square
Halve the coefficient of x, then square it.
The key idea
Halve the coefficient of x, then square it.
x² + 2hx + h² = (x + h)²
Worked examples
Complete x² + 68x + □ = (x + 34)².
(68 ÷ 2)² = 1156
1156
Complete x² + 66x + □ = (x + 33)².
(66 ÷ 2)² = 1089
1089
Try it yourself
Complete x² + 18x + □ = (x + 9)².
Complete x² + 22x + □ = (x + 11)².
Check your understanding
Answers and marking notes
- 81
(18 ÷ 2)² = 81
- 121
(22 ÷ 2)² = 121
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.