1. What is Completing the Square?

Completing the square is a method for solving quadratic equations by rewriting them in perfect square form. This technique is fundamental in algebra and provides insights into the properties of quadratic functions.

2. How Does the Calculator Work?

The calculator uses the completing the square formula:

Where:

• \( a \) — Coefficient of x² term (must be non-zero)
• \( b \) — Coefficient of x term
• \( c \) — Constant term

Explanation: The method transforms the equation \( ax^2 + bx + c = 0 \) into vertex form, revealing the roots directly.

3. Importance of Completing the Square

Details: This method is essential for deriving the quadratic formula, graphing parabolas, and solving optimization problems in calculus.

4. Using the Calculator

Tips: Enter coefficients a, b, and c from your quadratic equation. The calculator will display real solutions if they exist.

5. Frequently Asked Questions (FAQ)

Q1: What if the discriminant is negative?
A: The equation has no real solutions, but two complex solutions involving imaginary numbers.

Q2: How is this different from the quadratic formula?
A: The quadratic formula is derived from completing the square. Both methods give the same solutions.

Q3: When should I use completing the square?
A: It's particularly useful when you need the vertex form of a quadratic or when solving problems involving maximum/minimum values.

Q4: What if coefficient 'a' is not 1?
A: The calculator handles any non-zero value of 'a' by factoring it out in the process.

Q5: Can this solve all quadratic equations?
A: Yes, it can solve any quadratic equation with real or complex coefficients.