How do you solve quadratic equations using the quadratic formula?

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients from the equation ax² + bx + c = 0. Here's a step-by-step guide: 1. **Identify the coefficients**: First, ensure your equation is in standard form (ax² + bx + c = 0). Identify the values of a, b, and c. 2. **Calculate the discriminant**: The discriminant is b² - 4ac. This tells us about the nature of the roots: - If positive: two distinct real solutions - If zero: one repeated real solution - If negative: two complex solutions 3. **Substitute into the formula**: Plug your values of a, b, and c into the quadratic formula. 4. **Simplify**: Calculate the value under the square root first, then divide by 2a. **Example**: Solve 2x² + 5x - 3 = 0 - a = 2, b = 5, c = -3 - Discriminant = 5² - 4(2)(-3) = 25 + 24 = 49 - x = (-5 ± √49) / (2·2) = (-5 ± 7) / 4 - x₁ = (-5 + 7) / 4 = 2/4 = 1/2 - x₂ = (-5 - 7) / 4 = -12/4 = -3 The solutions are x = 1/2 and x = -3.