Completing the Square

Purpose:

Rewrite a quadratic expression into a square form.

Example 1:

x² + 4x + 1

x² + 4x + 4 − 4 + 1

= (x + 2)² − 3

Example 2:

2x² − 4x + 3

2(x² − 2x) + 3

2((x − 1)² − 1) + 3

= 2(x − 1)² + 1