X2 - 5x + 6 = 0

To solve the quadratic equation \( x^2 - 5x + 6 = 0 \), we can factor it. 1. We need to find two numbers that multiply to 6 (the constant term) and add up to -5 (the coefficient of x). The numbers that meet these criteria are -2 and -3 since: - \(-2 \times -3 = 6\) - \(-2 + -3 = -5\) 2. Now, we can factor the quadratic: \[ (x - 2)(x - 3) = 0 \] 3. Setting each factor equal to zero gives us: \[ x - 2 = 0 \quad \text{or} \quad x - 3 = 0 \] 4. Solving these equations, we find: \[ x = 2 \quad \text{and} \quad x = 3 \] Thus, the solutions to the equation \( x^2 - 5x + 6 = 0 \) are \( x = 2 \) and \( x = 3 \).