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

  1. Enter the coefficients **a**, **b**, and **c** for the equation $ax^2 + bx + c = 0$.
  2. Click **Complete the Square**.
  3. 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.

About

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.

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