Quadratic Formula Calculator

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Solve quadratic equations of the form ax² + bx + c = 0

Quadratic Equation Solver

ax² + bx + c = 0

Solution

x = -1, x = -2

Discriminant: 1 (Two real roots)

x = [-b ± √(b² - 4ac)] / 2a

Derivation of the Quadratic Formula

1. Start with the quadratic equation: ax² + bx + c = 0

2. Divide both sides by a: x² + (b/a)x + c/a = 0

3. Move the constant term to the right: x² + (b/a)x = -c/a

4. Complete the square: x² + (b/a)x + (b/2a)² = -c/a + (b/2a)²

5. Simplify: (x + b/2a)² = (b² - 4ac)/4a²

6. Take the square root: x + b/2a = ±√(b² - 4ac)/2a

7. Solve for x: x = [-b ± √(b² - 4ac)] / 2a