The Good News
I found today a question on Quora: someone has asked what the solution
for an equation of degree 5 is. According to the Abel-Ruffini theoremi,
there are no solutions in radicals for the general form of such equations.
The good news is that I found quickly that x=0 is one of the solution.
This leaves me with a biquadratic equation, for which a solution in radical
exists, but I do not care to even solve a cubic one using radicals because
the solutions found always look ugly. and the best way to deal with the
zeros found using the Cardano's method is to use a calculator and then
refer back to the equation and try assigning the result to the variable.
Well, I solved the biquadratic and cubic equations using good news, too.
Then, I had to solve a quadratic equation without without even completing
the square: you don't need it when the equation is x^2 + 1 = 0.