The characteristic equation gives $K=-s(s+2)(s+6)$. At a breakaway point $dK/ds=-(3s^2+16s+12)=0$, so $s=(-8\pm2\sqrt7)/3$. The valid real-axis branch between −2 and 0 contains $s=(-8+2\sqrt7)/3=-0.90283$. Substituting gives K = 5.049, rounding to 5.0. The other stationary point is not on a positive-K real-axis locus segment.
More Stability and frequency response: Bode plot, phase and gain margins, Routh and Nyquist criteria, root loci questions
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