$$x^2+ax+b = x^2+2x\frac{a}{2} + (\frac{a}{2})^2 - (\frac{a}{2})^2 +b = \bigg(x-\frac{a}{2}\bigg)^2+\bigg(b-\big(\frac{a}{2}\big)^2\bigg) \equiv y^2+c$$