Solve sqrt{x^3-4x^2-4x-1}=00

$$\sqrt{ { x }^{ 3 } -4 { x }^{ 2 } -4x-1 } =00$$

Solve for x (complex solution)

$$x=-\frac{2^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\left(-\sqrt[3]{3\left(9\sqrt{59}+299\sqrt{3}\right)}i-\sqrt[3]{3\sqrt{177}+299}+2\sqrt[3]{299-3\sqrt{177}}-4\sqrt[3]{2}+4\sqrt{3}\sqrt[3]{2}i\right)}{24}\approx -0.432268256+0.136797606i$$

$$x = \frac{2 ^ {\frac{2}{3}} {(\sqrt[3]{3 \sqrt{177} + 299} + \sqrt[3]{299 - 3 \sqrt{177}} + 4 \sqrt[3]{2})}}{6} \approx 4.864536512$$

$$x=-\frac{2^{\frac{2}{3}}\left(-\sqrt{3}i+1\right)\left(\sqrt[3]{3\left(9\sqrt{59}+299\sqrt{3}\right)}i-4\sqrt{3}\sqrt[3]{2}i-\sqrt[3]{3\sqrt{177}+299}+2\sqrt[3]{299-3\sqrt{177}}-4\sqrt[3]{2}\right)}{24}\approx -0.432268256-0.136797606i$$

Solve for x

$$x = \frac{2 ^ {\frac{2}{3}} {(\sqrt[3]{3 \sqrt{177} + 299} + \sqrt[3]{299 - 3 \sqrt{177}} + 4 \sqrt[3]{2})}}{6} = 4.864536512317583$$

$$-\frac{28\sqrt[3]{\frac{\sqrt{177}}{18}+\frac{299}{54}}}{9}+\frac{1}{27}\sqrt[3]{19683\times \frac{10976\sqrt{177}}{6561}+3281824}-\frac{28\sqrt[3]{-\frac{\sqrt{177}}{18}+\frac{299}{54}}}{9}+\frac{1}{27}\sqrt[3]{19683\left(-\frac{10976\sqrt{177}}{6561}\right)+3281824}\geq 0\text{ and }-\frac{28\sqrt[3]{\frac{\sqrt{177}}{18}+\frac{299}{54}}}{9}+\frac{1}{27}\sqrt[3]{19683\times \frac{10976\sqrt{177}}{6561}+3281824}-\frac{28\sqrt[3]{-\frac{\sqrt{177}}{18}+\frac{299}{54}}}{9}+\frac{1}{27}\sqrt[3]{19683\left(-\frac{10976\sqrt{177}}{6561}\right)+3281824}+1\geq 1$$