Some weird equations In our theoreticall class professor stated that from this equation $(C = constant)$
$$
x^2 + 4Cx - 2Cy = 0
$$
we can first get:
$$
x = \frac{-4C + \sqrt{16 C^2 - 4(-2Cy)}}{2}
$$
and than this one:
$$
x = 2C \left[\sqrt{1 + \frac{y}{2C}} -1\right] 
$$
How is this even possible?

Here's the algebra:
$$x^2 + 4Cx - 2Cy = (x+2C)^2-4C^2 - 2Cy = 0 $$
Thus:
$$
(x+2C)^2 = 4C^2 + 2Cy = 2C(2C+y).
$$
Take square roots:
$$
x_1 = -2C + \sqrt{2C(2C+y)} =\frac{-4C + \sqrt{16C^2 +8Cy}}{2}$$
and
$$
x_2 = -2C - \sqrt{2C(2C+y)}
$$
