1. What is Completing the Square?

Completing the square is a method for solving quadratic equations by rewriting them in perfect square form. It's a fundamental technique in algebra that's used to derive the quadratic formula.

2. How Does the Calculator Work?

The calculator uses the completing the square formula:

Where:

• \( b \) — Coefficient of the linear term
• \( c \) — Constant term

Explanation: The equation transforms \( x^2 + bx + c = 0 \) into perfect square form and solves for x.

3. Importance of Completing the Square

Details: This method is essential for solving quadratic equations, graphing parabolas, and understanding the derivation of the quadratic formula. It's also used in calculus for integration.

4. Using the Calculator

Tips: Enter the coefficients b and c from your quadratic equation in the form \( x^2 + bx + c = 0 \). The calculator will handle both real and complex solutions.

5. Frequently Asked Questions (FAQ)

Q1: What if I get complex solutions?
A: Complex solutions (with 'i') occur when the discriminant is negative, meaning no real solutions exist. The calculator will display both complex roots.

Q2: Can I use this for equations where a ≠ 1?
A: This calculator assumes the coefficient of x² is 1. For equations in the form ax² + bx + c = 0, first divide all terms by a.

Q3: Why is completing the square useful?
A: Beyond solving quadratics, it's used to find vertex form of parabolas, derive formulas, and solve problems in physics and engineering.

Q4: What's the difference between this and the quadratic formula?
A: The quadratic formula is derived from completing the square. This method shows the intermediate steps.

Q5: How accurate are the solutions?
A: Solutions are calculated to 4 decimal places. For exact form, consider symbolic algebra systems.