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:

\[ x = 4 \quad \text{and} \quad x = -2 \]