- TeX source:
- \begin{array}{ccrclcl}& & \mathbb{D} &=& \mathbb{R} \\\\\text{1. Zeile:} & & \dfrac{2}{e^{-x+1}} \left(x^2-x\right) &=& 40e^{x-1} \\\\\text{2. Zeile:} & & 2\left(x^2-x\right)e^{-(-x+1)} &=& 40e^{x-1} \\\\\text{3. Zeile:} & & \left(2x^2-2x\right)e^{x-1} &=& 40e^{x-1} & \vert & -40e^{x-1} \\\\\text{4. Zeile:} & & \left(2x^2-2x\right)e^{x-1}-40e^{x-1} &=& 0 \\\\\text{5. Zeile:} & & e^{x-1}\left(2x^2-2x-40\right) &=& 0 &\vert& \text{Satz vom Nullprodukt}\\\\\text{6. Zeile:} & \text{Faktor 1:} & e^{x-1} &=& 0 \\\\\\\text{7. Zeile:} & \text{Faktor 2:} & 2x^2-2x-40 &=& 0 & \vert& :2 \\\\& & x^2-x -20 &=& 0 & \vert& \text{p-q-Formel} \\\\& & x_{1,2}&=&\dfrac{1}{2}\pm\sqrt{\left(-\dfrac{1}{2}\right)^2+20}\\\\& & x_{1,2}&=&\dfrac{1}{2}\pm\sqrt{\dfrac{81}{4}}\\\\& & x_{1}&=&\dfrac{1}{2}+\dfrac{9}{2} = 5 \\\\ & & x_{2}&=&\dfrac{1}{2}-\dfrac{9}{2} = -4 \\\\\\& & \mathbb{L} &=& \{-4;5\}\end{array}