1. The problem is to simplify and solve the expression $$x = \frac{-(-5) + \sqrt{(-5)^2 - 4(2)(6)}}{2(2)}$$. 2. First, simplify the numerator's components: - The double negative: $-(-5) = 5$ - Calculate inside the square root: $$(-5)^2 = 25$$ - Calculate the product inside the square root: $$4 \times 2 \times 6 = 48$$ 3. Substitute these values back into the expression under the square root: $$\sqrt{25 - 48} = \sqrt{-23}$$ 4. Since the square root of a negative number involves imaginary numbers, rewrite it as: $$\sqrt{-23} = i\sqrt{23}$$ where $i$ is the imaginary unit. 5. Now the expression becomes: $$x = \frac{5 + i\sqrt{23}}{4}$$ 6. This is the simplified form of $x$ in terms of real and imaginary parts. Final answer: $$x = \frac{5}{4} + \frac{i\sqrt{23}}{4}$$