X2-2x-8=0

To solve the quadratic equation \( x^2 - 2x - 8 = 0 \), you can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] In this equation, \( a = 1 \), \( b = -2 \), and \( c = -8 \). First, calculate the discriminant \( b^2 - 4ac \): \[ b^2 - 4ac = (-2)^2 - 4(1)(-8) = 4 + 32 = 36 \] Now, substitute back into the quadratic formula: \[ x = \frac{-(-2) \pm \sqrt{36}}{2(1)} = \frac{2 \pm 6}{2} \] This gives us two solutions: 1. \( x = \frac{2 + 6}{2} = \frac{8}{2} = 4 \) 2. \( x = \frac{2 - 6}{2} = \frac{-4}{2} = -2 \) Therefore, the solutions to the equation \( x^2 - 2x - 8 = 0 \) are: \[ x = 4 \quad \text{and} \quad x = -2 \]