Question

The steps to solving the quadratic equation (x^2 - 5x + 6 = 0) by factoring. Identify the coefficients: In the equation (x^2 - 5x + 6 = 0), the coefficients are (a = 1), (b = -5), and (c = 6). Factor the equation: We’re looking for two numbers that multiply to (c) (which is 6) and add up to (b) (which is -5). The numbers that satisfy these conditions are -2 and -3. So, we can write the equation as ((x - 2)(x - 3) = 0). Solve for x: Now, we have two simple equations (x - 2 = 0) and (x - 3 = 0). Solving these gives us the solutions (x = 2) and (x = 3). Factoring: If the quadratic equation can be easily factored, this method is often the quickest. For example, the equation (x^2 - 5x + 6 = 0) can be factored into ((x - 2)(x - 3) = 0). Completing the Square: This method involves rearranging the equation into a perfect square trinomial, which can then be solved relatively easily. This is particularly useful when the coefficient of (x^2) is 1. Quadratic Formula: The quadratic formula can be used to solve any quadratic equation. It’s a good method to use when the equation is hard to factor or when you want to get an exact solution. Graphing: If you’re more visually inclined, you might prefer to solve the equation by graphing. The solutions to the equation are the x-intercepts of the graph.