To solve the quadratic equation \( x^2 - 5x + 6 = 0 \) using the quadratic formula, follow these steps: 1. Identify coefficients: In the equation \( ax^2 + bx + c = 0 \), we have: \( a = 1 \) \( b = -5 \) \( c = 6 \) 2. Quadratic formula: The quadratic formula is given by: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] 3. Calculate the discriminant: First, calculate \( b^2 - 4ac \): \[ b^2 - 4ac = (-5)^2 - 4(1)(6) = 25 - 24 = 1 \] 4. Substitute values into the formula: \[ x = \frac{-(-5) \pm \sqrt{1}}{2(1)} = \frac{5 \pm 1}{2} \] 5. Calculate the two possible values for \( x \): For \( x_1 \): \[ x_1 = \frac{5 + 1}{2} = \frac{6}{2} = 3 \] For \( x_2 \): \[ x_2 = \frac{5 - 1}{2} = \frac{4}{2} = 2 \] 6. Final solutions: The solutions to the equation \( x^2 - 5x + 6 = 0 \) are: \[ x = 3 \quad \text{and} \quad x = 2 \]