Completing the Square Calculator
Convert any quadratic equation into its vertex form and find the roots by completing the square. Perfect for students and algebra practice.
Method:
1. Divide by 'a'
2. Add (b/2a)² to both sides
3. Rewrite as (x + b/2a)² = constant
For x² + 6x + 5 = 0: (x + 3)² - 9 + 5 = 0 (x + 3)² = 4 x + 3 = ±2 → x = -1, -5
What does "completing the square" mean?
Completing the square is a technique used to solve quadratic equations by turning a quadratic expression into a perfect square trinomial plus a constant.
When should I use completing the square?
It is useful for finding the vertex of a parabola, converting standard form equations to vertex form, and solving quadratic equations where the quadratic formula might be more cumbersome.
What is the formula for the "added" term?
To complete the square for x² + bx, you add (b/2)². This creates the perfect square (x + b/2)².
Can this method solve any quadratic equation?
Yes, completing the square can be used to solve any quadratic equation, regardless of whether the roots are real or complex.
🔗 Related Calculators
📐 Formula
Method:
1. Divide by 'a'
2. Add (b/2a)² to both sides
3. Rewrite as (x + b/2a)² = constant
📝 Example Calculation
For x² + 6x + 5 = 0: (x + 3)² - 9 + 5 = 0 (x + 3)² = 4 x + 3 = ±2 → x = -1, -5
❓ Frequently Asked Questions
What does "completing the square" mean?▼
Completing the square is a technique used to solve quadratic equations by turning a quadratic expression into a perfect square trinomial plus a constant.
When should I use completing the square?▼
It is useful for finding the vertex of a parabola, converting standard form equations to vertex form, and solving quadratic equations where the quadratic formula might be more cumbersome.
What is the formula for the "added" term?▼
To complete the square for x² + bx, you add (b/2)². This creates the perfect square (x + b/2)².
Can this method solve any quadratic equation?▼
Yes, completing the square can be used to solve any quadratic equation, regardless of whether the roots are real or complex.