How to find the point on the root locus with a certain damping in Octave

[FlatAssembler]

So, allegedly, for the gain of 0.723288, the damping is equal to 0.689481 (very close to the required damping of 0.7), and the frequency is 0.104 rad/sec. How do I check whether that's true?

As early as my first semesters at university i figured (and was told by my profs) that anyone calculating 6 digit numbers trying to solve a 2 digit number problem has no idea what he is doing.

We were also taught that in our high-school chemistry classes. But in our university physics classes, we were taught that real science uses error margins in inputs, and that it claculates the error margins of the results using the partial derivatives of the formulas.