x²-8x-9=0

To solve the quadratic equation \( x^2 - 8x - 9 = 0 \), we can use the quadratic formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

In this equation, \( a = 1 \), \( b = -8 \), and \( c = -9 \).

1. Calculate the discriminant: \[ b^2 - 4ac = (-8)^2 - 4(1)(-9) = 64 + 36 = 100 \]

2. Now plug the values into the quadratic formula: \[ x = \frac{-(-8) \pm \sqrt{100}}{2(1)} = \frac{8 \pm 10}{2} \]

3. This gives us two potential solutions:

   • For the positive case: \[ x = \frac{8 + 10}{2} = \frac{18}{2} = 9 \]
   • For the negative case: \[ x = \frac{8 - 10}{2} = \frac{-2}{2} = -1 \]

Thus, the solutions to the equation \( x^2 - 8x - 9 = 0 \) are \( x = 9 \) and \( x = -1 \).