Question

c. \\(dfrac{-6 + sqrt{(-6)^2 - 4(2)(5)}}{2}\\)

Explanation:

Step1: Calculate discriminant inside root

First compute the terms under the square root:
$\sqrt{(-6)^2 - 4(2)(5)} = \sqrt{36 - 40}$

Step2: Simplify the root term

Simplify the expression inside the square root:
$\sqrt{36 - 40} = \sqrt{-4} = 2i$

Step3: Substitute back and simplify numerator

Combine the terms in the numerator:
$-6 + 2i$

Step4: Divide by denominator

Divide the entire numerator by 2:
$\frac{-6 + 2i}{2} = -3 + i$

Answer:

$-3 + i$