X²-14X+24=0

To solve the quadratic equation \( X^2 - 14X + 24 = 0 \), you can use the quadratic formula: \[ X = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] where \( a = 1 \), \( b = -14 \), and \( c = 24 \). 1. First, calculate the discriminant (\( b^2 - 4ac \)): \[ b^2 - 4ac = (-14)^2 - 4(1)(24) = 196 - 96 = 100 \] 2. Now, plug the values into the quadratic formula: \[ X = \frac{-(-14) \pm \sqrt{100}}{2(1)} \] \[ X = \frac{14 \pm 10}{2} \] 3. This gives us two possible values for \( X \): \[ X = \frac{14 + 10}{2} = \frac{24}{2} = 12 \] \[ X = \frac{14 - 10}{2} = \frac{4}{2} = 2 \] Thus, the solutions to the equation \( X^2 - 14X + 24 = 0 \) are \( X = 12 \) and \( X = 2 \).