-x2-8x+9=0

To solve the quadratic equation \(-x^2 - 8x + 9 = 0\), we can first multiply the entire equation by -1 to make the leading coefficient positive:

\[ x^2 + 8x - 9 = 0 \]

Now we can use the quadratic formula, which is given by:

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

Here, \(a = 1\), \(b = 8\), and \(c = -9\). Plugging these values into the formula:

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

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

3. Calculate the two possible solutions:

   • First solution: \[ x = \frac{-8 + 10}{2} = \frac{2}{2} = 1 \]
   • Second solution: \[ x = \frac{-8 - 10}{2} = \frac{-18}{2} = -9 \]

So the solutions to the equation \(-x^2 - 8x + 9 = 0\) are:

\[ x = 1 \quad \text{and} \quad x = -9 \]