Completing the Square Calculator
Solution Steps
How to Use
- Enter the coefficients of your quadratic equation in the form ax² + bx + c = 0
- Click the "Solve" button
- View the step-by-step solution
About Completing the Square
Completing the square is a method to solve quadratic equations by:
- Dividing all terms by a (if a ≠ 1)
- Moving the constant term to the right side
- Adding (b/2)² to both sides
- Factoring the left side as a perfect square
- Solving for x
Benefits:
- Works for all quadratic equations
- Helps understand the quadratic formula
- Useful for finding vertex form
- Important in calculus and physics
Common Examples
| Equation | Solution |
|---|---|
| x² + 6x + 8 = 0 | x = -2 or x = -4 |
| x² - 4x + 4 = 0 | x = 2 (double root) |
| 2x² + 4x - 6 = 0 | x = 1 or x = -3 |
| x² + 2x + 5 = 0 | x = -1 ± 2i |
Tips
- Make sure a ≠ 0 (not a quadratic equation if a = 0)
- If a ≠ 1, divide all terms by a first
- Remember to add (b/2)² to both sides
- Check your answer by substituting back
- Watch out for complex solutions
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