Solve the quadratic equation. \( -x^{2}+2 x-2=0 \) Write one exact, simplified solution in each box. You can add or remove boxes. If a solution is not a real number, write it in the form a + bi or \( \mathrm{a}-\mathrm{bi} \), where a and b are real numbers. \( \frac{\square}{\square} \)

To solve the quadratic equation \( -x^{2}+2 x-2=0 \), we can first multiply the entire equation by -1 to make it easier to work with: \( x^{2} - 2x + 2 = 0 \). Next, we can apply the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1, b = -2, \) and \( c = 2 \). Calculating the discriminant: \( b^2 - 4ac = (-2)^2 - 4(1)(2) = 4 - 8 = -4 \). Since the discriminant is negative, we will have complex solutions. Now, substituting values into the quadratic formula: \( x = \frac{2 \pm \sqrt{-4}}{2(1)} = \frac{2 \pm 2i}{2} = 1 \pm i \). Thus, the two solutions are: \( \frac{1 + i}{\square} \) and \( \frac{1 - i}{\square} \).