1. What is Completing the Square?

Completing the square is a method for solving quadratic equations by rewriting them in a perfect square trinomial form. It's a fundamental technique in algebra that provides insights into the nature of quadratic solutions.

2. How Does the Calculator Work?

The calculator uses the completing the square formula:

Where:

• \( a \) — Coefficient of x² term
• \( b \) — Coefficient of x term
• \( c \) — Constant term

Explanation: The method transforms the quadratic equation ax² + bx + c = 0 into vertex form, revealing the roots directly.

3. Importance of Completing the Square

Details: This technique is essential for deriving the quadratic formula, graphing parabolas, solving optimization problems, and understanding quadratic functions' properties.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation in the form ax² + bx + c = 0. The calculator will provide exact solutions, including complex roots when necessary.

5. Frequently Asked Questions (FAQ)

Q1: Why use completing the square instead of the quadratic formula?
A: While both methods work, completing the square helps understand the derivation of the quadratic formula and provides the vertex form directly.

Q2: What if I get complex solutions?
A: Complex solutions (with 'i') indicate the parabola doesn't intersect the x-axis. These are valid mathematical solutions.

Q3: Can a be zero?
A: No, if a=0, the equation is linear, not quadratic. The calculator requires a non-zero value for a.

Q4: How accurate are the solutions?
A: Solutions are calculated with high precision (4 decimal places), though exact form might be more precise for some equations.

Q5: What's the advantage over factoring?
A: Completing the square works for all quadratics, even those that don't factor neatly with rational numbers.