1. What is Solving by Taking Square Roots?

This method solves quadratic equations of the form ax² = c by isolating x² and taking the square root of both sides. The solution includes both positive and negative roots since squaring either value gives the same result.

2. How Does the Calculator Work?

The calculator uses the square root principle:

Where:

• \( x \) — The unknown variable
• \( c \) — The constant term
• \( \pm \) — Indicates both positive and negative roots

Explanation: For any equation in the form x² = c, the solutions are the positive and negative square roots of c.

3. When to Use This Method

Details: This method works for any quadratic equation that can be rewritten in the form x² = c. It's particularly useful when the equation has no linear (x) term.

4. Using the Calculator

Tips: Enter the value of c from your equation in the form x² = c. The calculator will provide both roots if they exist (when c ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What if c is negative?
A: The equation has no real solutions (but has complex solutions involving imaginary numbers).

Q2: Can this solve equations like x² + 4 = 13?
A: Yes, first rewrite as x² = 9 by subtracting 4 from both sides, then take square roots.

Q3: Why are there two solutions?
A: Because both positive and negative values squared give the same result (e.g., 3² = 9 and (-3)² = 9).

Q4: How precise are the solutions?
A: Solutions are rounded to 4 decimal places for practical use.

Q5: Can this solve more complex quadratics?
A: Only if they can be simplified to the form x² = c. For others, use factoring or quadratic formula.