Beispiel Nr: 10
$\text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ x^2-1x =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l|l} \begin{array}{l} \text{x-Ausklammern}\\ \hline 1x^{2}-1x =0 \\ x(1x -1)=0 \\ \\ 1 x-1 =0 \qquad /+1 \\ 1 x= 1 \qquad /:1 \\ x=\displaystyle\frac{1}{1}\\ x_1=0\\ x_2=1 \end{array}& \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ 1x^{2}-1x+0 =0 \\ x_{1/2}=\displaystyle\frac{+1 \pm\sqrt{\left(-1\right)^{2}-4\cdot 1 \cdot 0}}{2\cdot1} \\ x_{1/2}=\displaystyle \frac{+1 \pm\sqrt{1}}{2} \\ x_{1/2}=\displaystyle \frac{1 \pm1}{2} \\ x_{1}=\displaystyle \frac{1 +1}{2} \qquad x_{2}=\displaystyle \frac{1 -1}{2} \\ x_{1}=1 \qquad x_{2}=0 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ \\ x^{2}-1x+0 =0 \\ x_{1/2}=\displaystyle -\frac{-1}{2}\pm\sqrt{\left(\frac{\left(-1\right)}{2}\right)^2- 0} \\ x_{1/2}=\displaystyle \frac{1}{2}\pm\sqrt{\frac{1}{4}} \\ x_{1/2}=\displaystyle \frac{1}{2}\pm\frac{1}{2} \\ x_{1}=1 \qquad x_{2}=0 \end{array}\\ \end{array}$