Completing the Square

Examples, solutions, and videos to help GCSE Maths and Algebra students learn how to complete the square.

The following diagram shows the formula for Completing the Square. Scroll down the page for more examples and solutions of how to complete the square.

 

Completing the Square
Coefficient of x² = 1
Examples:
Express the following in the form (x+a)² + b
x² + 8x - 1
x² - 10x + 3
x² + 3x - 2
x² + 12x - 5
x² - 5x + 1

Completing the Square
Coefficient of x² > 1
Examples:
Express the following in the form (x+a)² + b
3x² - 12x + 5
2x² - x - 1
2x² + 12x - 3
5x² + 3x - 2

Completing the Square
Coefficient of x² < 1
Examples:
Express the following in the form (x+a)² + b
5 - 8x - x²
5 + 12x - 2x²
4 + 10x - x²
1 - 3x - 5x²

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