Final answer:
The quadratic equation can be solved by factoring into two linear factors: x = -b/2a ± √(b^2-4ac)/2a.
Explanation:
In order to solve a quadratic equation by factoring, we must first understand the basic form of a quadratic equation: ax^2 + bx + c = 0. The variables a, b, and c represent the coefficients of the equation. In order to solve for the roots of the equation, we must find the values of x that make the equation equal to 0.
To begin factoring, we must find two numbers that multiply to equal the constant term (c) and add to equal the coefficient of the linear term (b). These two numbers will then be used as the coefficients of the two linear factors. For example, if the equation is x^2 + 3x + 2 = 0, we must find two numbers that multiply to equal 2 and add to equal 3. In this case, the numbers are 1 and 2.
Once we have found the two numbers, we can rewrite the equation as (x + 1)(x + 2) = 0. This form allows us to easily solve for the roots of the equation. We can set each factor equal to 0 and solve for x. This gives us two values for x: x = -1 and x = -2.
Therefore, the final answer to the quadratic equation is x = -b/2a ± √(b^2-4ac)/2a. The ± symbol represents the two possible solutions, one with a positive sign and one with a negative sign.
In conclusion, solving a quadratic equation by factoring involves finding two numbers that multiply to equal the constant term and add to equal the coefficient of the linear term. These numbers are then used as the coefficients for the two linear factors, which can be set equal to 0 and solved for x. The final answer is a formula that can be used to find the two possible roots of the equation.