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.
In this case, the quadratic equation (x^2 - 5x + 6 = 0) can be quickly solved by factoring. The coefficients are (a = 1), (b = -5), and (c = 6). By factoring the equation, we find that ((x - 2)(x - 3) = 0). Solving for x gives us the solutions (x = 2) and (x = 3). This method is efficient and straightforward when the equation is easily factorable. Other methods such as completing the square, using the quadratic formula, or graphing can also be used depending on the specific situation and preferences of the solver.
