1. What is the Completing the Square Method?

The completing the square method is a technique for solving quadratic equations by rewriting them in perfect square form. This approach provides insight into the nature of the roots and is the basis for the quadratic formula.

2. How Does the Calculator Work?

The calculator uses the completing the square formula:

Where:

• \( a \) — Coefficient of x² (must not be zero)
• \( b \) — Coefficient of x
• \( c \) — Constant term

Explanation: The equation is derived by completing the square of the standard quadratic equation \( ax^2 + bx + c = 0 \).

3. Importance of Quadratic Equations

Details: Quadratic equations appear frequently in physics, engineering, economics, and many other fields. Understanding their solutions is fundamental to mathematics and its applications.

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 handle both real and complex roots.

5. Frequently Asked Questions (FAQ)

Q1: What if I get complex roots?
A: Complex roots (containing 'i') occur when the discriminant is negative, meaning the parabola doesn't intersect the x-axis.

Q2: Why can't coefficient 'a' be zero?
A: If a=0, the equation becomes linear (bx + c = 0), not quadratic.

Q3: How accurate are the results?
A: Results are rounded to 4 decimal places for readability while maintaining good precision.

Q4: Can I use this for any quadratic equation?
A: Yes, this method works for all quadratic equations, though some forms may be easier to factor.

Q5: What's the advantage over the quadratic formula?
A: This is actually how the quadratic formula is derived! The completing square method provides insight into the equation's structure.