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