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
Hey Peter_Schemer, good to see you again. Here are the solutions using the factorization method: a) x^2 + 8x + 12 = 0 Step 1: Find two numbers that multiply to 12 (the constant term) and add up to 8 (the coefficient of the x term). The numbers are 6 and 2. Step 2: Rewrite the middle term using these two numbers. x^2 + 6x + 2x + 12 = 0 Step 3: Group the terms and factor out the common factors from each group. x(x+6) + 2(x+6) = 0 Step 4: Factor out the common binomial factor (x+6). (x+6)(x+2) = 0 Step 5: Set each factor equal to zero and solve for x. x+6 = 0 or x+2 = 0 x = -6 or x = -2 The solutions are x = -6, x = -2. b) x^2 - 6x + 5 = 0 Step 1: Find two numbers that multiply to 5 (the constant term) and add up to -6 (the coefficient of the x term). The numbers are -1 and -5. Step 2: Rewrite the middle term using these two numbers. x^2 - 1x - 5x + 5 = 0 Step 3: Group the terms and factor out the common factors from each group. x(x-1) - 5(x-1) = 0 Step 4: Factor out the common binomial factor (x-1). (x-1)(x-5) = 0 Step 5: Set each factor equal to zero and solve for x. x-1 = 0 or x-5 = 0 x = 1 or x = 5 The solutions are x = 1, x = 5. Drop the next question 📸