A unit$-$feedback control system has the forward$-$path transfer function:

G$($s$)=[$K$($s$+5)]/[$s$($s$+7)($s$^2+2$s $+5)]$

please refer to the following steps to construct the root locus for K$>=0$ by hand drawing. For $($i$)$~$($vii$),$ write down your calculation$/$derivation process or reasons.

$($i$)$Find the zeros and poles,if any.

$($ii$)$Find the root loci on the real axis,if any.

$($iii$)$Find angles of asymptotes,if any.

$($iv$)$Find the intersection of asymptotes $,$if any.

$($vi$)$Find the breakaway points,if any.Then,find the values of K for all breakaway points.

$($vii$)$If there are complex poles or zeros,find the angle of departure and angle of arrival.

$($vii$)$Complete your root locus drawing.Show the result.