X²-10x+24=0

To solve the quadratic equation \( x^2 - 10x + 24 = 0 \), we can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] In this equation, \( a = 1 \), \( b = -10 \), and \( c = 24 \). 1. Calculate the discriminant \( b^2 - 4ac \): \[ b^2 - 4ac = (-10)^2 - 4 \cdot 1 \cdot 24 = 100 - 96 = 4 \] 2. Now substitute the values into the quadratic formula: \[ x = \frac{-(-10) \pm \sqrt{4}}{2 \cdot 1} = \frac{10 \pm 2}{2} \] 3. This gives us two possible solutions: \[ x = \frac{10 + 2}{2} = \frac{12}{2} = 6 \] \[ x = \frac{10 - 2}{2} = \frac{8}{2} = 4 \] Thus, the solutions to the equation \( x^2 - 10x + 24 = 0 \) are: \[ x = 6 \quad \text{and} \quad x = 4 \]