X2-9x+14=0

To solve the quadratic equation \(x^2 - 9x + 14 = 0\), we can use the factoring method. 1. First, we look for two numbers that multiply to \(14\) (the constant term) and add up to \(-9\) (the coefficient of \(x\)). 2. The numbers that satisfy these conditions are \(-7\) and \(-2\) because: - \(-7 \times -2 = 14\) - \(-7 + (-2) = -9\) 3. We can now factor the equation as: \[ (x - 7)(x - 2) = 0 \] 4. Setting each factor equal to zero gives us the solutions: \[ x - 7 = 0 \quad \Rightarrow \quad x = 7 \] \[ x - 2 = 0 \quad \Rightarrow \quad x = 2 \] So, the solutions to the equation \(x^2 - 9x + 14 = 0\) are \(x = 7\) and \(x = 2\).