Why does the quadratic formula give solution to quadratic equation
Let the quadratic equation be of the form: ax2 + bx + c = 0.
Now by completing the square ( which can be done numeorous ways) get: a(x - b / 2a)2 - a(b / 2a)2 + c = 0.
Then rearrange equation:
a(x - b / 2a)2 = a(b / 2a)2 + c, x - (b / 2a) = +- sqrt( (ab2 - 4a2c) / 4a3) and hence x = (- b +- sqrt(b2 - 4ac)) / 2a
