$$ a x^2 + b x + c = 0 $$
Stap 1. Neem aan dat $a \ne 0$ : $$ x^2 + \frac{b}{a} x + \frac{c}{a} = 0 $$ Stap 2. Zoals in $\,x^2 + 2A x + A^2 = (x+A)^2$ , waarin $\,A = b/(2a)$ : $$ x^2 + 2\frac{b}{2a} x + \left(\frac{b}{2a}\right)^2 - \left(\frac{b}{2a}\right)^2 + \frac{c}{a} = 0 $$ Stap 3: $$ \left(x + \frac{b}{2a}\right)^2 - \left(\frac{b}{2a}\right)^2 + \frac{c}{a} = 0 $$ Stap 4: $$ \left(x + \frac{b}{2a}\right)^2 = \left(\frac{b}{2a}\right)^2 - \frac{c}{a} $$ Stap 5: $$ \left(x + \frac{b}{2a}\right)^2 = \frac{b^2}{4a^2} - \frac{c}{a} = \frac{b^2}{4a^2} - \frac{4ac}{4a^2} = \frac{b^2-4ac}{4a^2} $$ Stap 6: $$ x + \frac{b}{2a} = \pm \frac{\sqrt{b^2-4ac}}{2a} $$ Stap 7: $$ x = - \frac{b}{2a} \pm \frac{\sqrt{b^2-4ac}}{2a} $$ Stap 8: $$ x = \frac{- b \pm \sqrt{b^2-4ac}}{2a} $$