Solve using the quadratic formula: x2 - 2x - 24 = 0

Step-by-Step Solution

To solve the quadratic equation x^2 - 2x - 24 = 0 using the quadratic formula, follow these steps:

1. Identify the coefficients: The standard form of a quadratic equation is ax^2 + bx + c = 0. For your equation, a = 1, b = -2, and c = -24.

2. Apply the quadratic formula: The quadratic formula is x = (-b +/- sqrt(b^2 - 4ac)) / (2a). Substitute the values: x = (-(-2) +/- sqrt((-2)^2 - 4 * 1 * -24)) / (2 * 1)

3. Simplify the expression: x = (2 +/- sqrt(4 + 96)) / 2 x = (2 +/- sqrt(100)) / 2 x = (2 +/- 10) / 2

4. Find the two roots:

   • Root 1: x = (2 + 10) / 2 = 12 / 2 = 6

   • Root 2: x = (2 - 10) / 2 = -8 / 2 = -4