1. What is Completing the Square?

Completing the square is a method for solving quadratic equations by rewriting them in perfect square form. The Symbolab method provides a systematic approach to this algebraic technique.

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 equation transforms the standard quadratic form ax² + bx + c = 0 into vertex form by completing the square.

3. Importance of Completing the Square

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

4. Using the Calculator

Tips: Enter coefficients a, b, and c from your quadratic equation ax² + bx + c = 0. The calculator will provide real or complex solutions.

5. Frequently Asked Questions (FAQ)

Q1: Why use Symbolab's method?
A: Symbolab's approach provides a clear, step-by-step process that's particularly helpful for learning the technique.

Q2: What if I get complex numbers?

A: If the discriminant (b² - 4ac) is negative, the solutions will be complex conjugates, shown with "i" for √(-1).

Q3: Can this solve all quadratic equations?
A: Yes, this method works for all quadratic equations, including those with complex roots.

Q4: How is this different from the quadratic formula?
A: The quadratic formula is derived from completing the square - they give identical results but through different approaches.

Q5: What if a = 0?
A: If a = 0, the equation is linear, not quadratic. The calculator will show an error in this case.