Math & Algebra Tool
Completing the Square
Solve quadratic equations by transforming them into a perfect square trinomial.
x² + x + = 0
Σ The Formula
x² + bx + (b/2)² = (x + b/2)²
Real World Examples
Standard Quadratic
x² + 6x + 5 = 0 → (x+3)² = 4 → x = -1, -5
Vertex Form
Learn how to convert standard form to vertex form step-by-step.
# About This Calculator
Completing the Square is a fundamental algebraic technique used to solve quadratic equations, derive the quadratic formula, and convert quadratic functions from standard form ($ax^2 + bx + c$) to vertex form ($a(x-h)^2 + k$).
The core idea is to add a specific value to both sides of the equation to make the quadratic part a "perfect square trinomial." This allows you to easily isolate $x$ by taking the square root.
How To Use
- Enter the coefficients **a**, **b**, and **c** for the equation $ax^2 + bx + c = 0$.
- Click **Complete the Square**.
- Follow the step-by-step breakdown as the constant is moved, the square is found, and the roots are calculated.
Frequently Asked Questions
When should I use this over the Quadratic Formula?+
Completing the square is often most efficient when the coefficient of x² is 1 and the coefficient of x is an even number. It is also required for certain calculus operations like integration by parts.
Can it solve any quadratic?+
Yes, any quadratic equation can be solved using this method, even those with complex roots (though this tool focuses on real number results).
Is Completing the Square free to use?+
Yes, Completing the Square on Matheric is completely free to use. We believe in accessible education and utility for everyone.
How accurate is Completing the Square?+
We use standard mathematical formulas and high-precision computing algorithms to ensure results for Completing the Square are accurate for academic and professional use.
Can I use Completing the Square on my phone?+
Yes! Completing the Square is fully responsive and optimized for all devices, including smartphones, tablets, and desktops.
Do you save my data?+
No. We prioritize your privacy. All calculations are performed in your browser or temporarily processed, and we do not store your personal input data.