\[
G' = \frac{K}{s(5s+1)(10s+1)+K} = \frac{K}{50s^3+15s^2+s+K}
\]
\[
= \frac{K}{K-15\omega^2+(\omega-50\omega^3)j} = \frac{K\left[K-15\omega^2-(\omega-50\omega^3)j\right]}{(K-15\omega^2)^2+(\omega-50\omega^3)^2}
\]
\[
\begin{cases}
\omega - 50\omega^3 = 0 \Rightarrow \omega_x = \dfrac{1}{\sqrt{50}} \\[2mm]
RE = \dfrac{K}{K-\dfrac{15}{50}} = -0.25 \Rightarrow K = 0.06
\end{cases}
\]