The classic approach to solve a quadratic equation of the form
Is the method of the quadratic extension. Therefore we first divide the whole equation by A and get
Now the idea is to get to a form of (x + G)^2 = H. therefore we add B^2/(4 A^2). This term is called the quadratic extension and out equation looks like
Now the left part is a binomial and this can be written as
Or with the right part brought to one line
The root on both sides is
And resolved for x
Basically that’s it.
But there are special cases:
If B2 < 4AC the root will be imaginary and we get 2 conjugate complex results as
So a sample equation of
x2 – 2x + 5 = 0
has the 2 solutions
x1 = 1 + j2
x2 = 1 – j2