Formula
x² + bx + c = (x + b/2)² − (b/2)² + c
Completing the square rewrites the quadratic in a form from which the vertex and roots can be identified quickly.
Example
x² + 6x + 5 = (x + 3)² − 4, so the vertex is (−3, −4).
FAQs
Why complete the square?
It makes solving quadratics easier and reveals the vertex of a parabola.
Does it always work?
Yes. Any quadratic expression can be rewritten in completed-square form.