1. What is Completing the Square?

Completing the square is a method for solving quadratic equations by converting them into perfect square trinomials. This technique is fundamental in algebra and provides insights into the nature of quadratic solutions.

2. How Does the Calculator Work?

The calculator uses the quadratic formula derived from completing the square:

Where:

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

Explanation: The method transforms the quadratic equation ax² + bx + c = 0 into the form (x + d)² = e, where d and e are constants.

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 ax² + bx + c = 0. Coefficient a cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: Why complete the square when we have the quadratic formula?
A: Completing the square helps understand where the quadratic formula comes from and is useful for other applications like conic sections.

Q2: What if the discriminant is negative?
A: The calculator will show complex solutions with imaginary numbers (i = √-1).

Q3: Can I use this for equations with a ≠ 1?
A: Yes, the calculator handles any non-zero value of a.

Q4: What are real-world applications?
A: Used in physics for projectile motion, engineering for structural analysis, and economics for profit maximization.

Q5: How accurate are the results?
A: Results are accurate to 4 decimal places, sufficient for most practical purposes.