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
The solutions to the equation x^2 - 5x + 6 = 0 are x=2 and x=3. Steps to solve by factoring: 1. Identify coefficients: The quadratic equation is in the form ax^2 + bx + c = 0, where a=1, b=-5, and c=6. 2. Find two numbers: We need to find two numbers that multiply to c (which is 6) and add up to b (which is -5). The numbers are -2 and -3, because (-2) × (-3) = 6 and (-2) + (-3) = -5. 3. Factor the quadratic: Rewrite the equation using these numbers: (x - 2)(x - 3) = 0 4. Set each factor to zero: For the product of two factors to be zero, at least one of the factors must be zero. x - 2 = 0 or x - 3 = 0 5. Solve for x: x = 2 or x = 3