This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Joseph, let's knock this out. To solve the quadratic equation x^2 - x - 6 = 0 by factoring: Step 1: Identify two numbers that multiply to the constant term (-6) and add up to the coefficient of the x term (-1). The two numbers are 2 and -3, because 2 × (-3) = -6 and 2 + (-3) = -1. Step 2: Rewrite the middle term using these two numbers. x^2 + 2x - 3x - 6 = 0 Step 3: Factor by grouping. Group the first two terms and the last two terms. (x^2 + 2x) - (3x + 6) = 0 Factor out the common term from each group. x(x + 2) - 3(x + 2) = 0 Step 4: Factor out the common binomial (x+2). (x - 3)(x + 2) = 0 Step 5: Set each factor equal to zero and solve for x. x - 3 = 0 or x + 2 = 0 x = 3 or x = -2 The solutions are x = 3 and x = -2. The final answers are x = 3, x = -2. What's next?