Solve frac{-6+-sqrt{-6^2-4-6-5}}{2}

$$\frac{ -6+- \sqrt{ - { 6 }^{ 2 } -4-6-5 } }{ 2 }$$

Evaluate (complex solution)

$$-\frac{\sqrt{51}i}{2}-3\approx -3-3.570714214i$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$\frac{-6-\sqrt{-36-4-6-5}}{2}$$

Subtract 4 from -36 to get -40.

$$\frac{-6-\sqrt{-40-6-5}}{2}$$

Subtract 6 from -40 to get -46.

$$\frac{-6-\sqrt{-46-5}}{2}$$

Subtract 5 from -46 to get -51.

$$\frac{-6-\sqrt{-51}}{2}$$

Factor -51=51\left(-1\right). Rewrite the square root of the product \sqrt{51\left(-1\right)} as the product of square roots \sqrt{51}\sqrt{-1}. By definition, the square root of -1 is i.

$$\frac{-6-\sqrt{51}i}{2}$$

Multiply -1 and i to get -i.

$$\frac{-6-i\sqrt{51}}{2}$$

Evaluate

$$\text{Indeterminate}$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$\frac{-6-\sqrt{-36-4-6-5}}{2}$$

Subtract 4 from -36 to get -40.

$$\frac{-6-\sqrt{-40-6-5}}{2}$$

Subtract 6 from -40 to get -46.

$$\frac{-6-\sqrt{-46-5}}{2}$$

Subtract 5 from -46 to get -51.

$$\frac{-6-\sqrt{-51}}{2}$$

Real Part (complex solution)

$$-3$$