\(\begin{cases} \frac{c}{b} - \frac{b - \left(-b\right)}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{(2 * \left(\frac{c}{b} \cdot a\right) + \left(\left(-b\right) - b\right))_*} & \text{otherwise} \end{cases}\)
- Started with
\[\begin{cases} \frac{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{otherwise} \end{cases}\]
40.8
- Applied taylor to get
\[\begin{cases} \frac{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)} & \text{otherwise} \end{cases}\]
23.4
- Taylor expanded around -inf to get
\[\begin{cases} \frac{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{\color{red}{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)}} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{\color{blue}{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)}} & \text{otherwise} \end{cases}\]
23.4
- Applied taylor to get
\[\begin{cases} \frac{\left(-b\right) - \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{\left(-b\right) - \left(b - 2 \cdot \frac{c \cdot a}{b}\right)}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)} & \text{otherwise} \end{cases}\]
10.1
- Taylor expanded around inf to get
\[\begin{cases} \frac{\left(-b\right) - \color{red}{\left(b - 2 \cdot \frac{c \cdot a}{b}\right)}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)} & \text{otherwise} \end{cases} \leadsto \begin{cases} \frac{\left(-b\right) - \color{blue}{\left(b - 2 \cdot \frac{c \cdot a}{b}\right)}}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)} & \text{otherwise} \end{cases}\]
10.1
- Applied simplify to get
\[\color{red}{\begin{cases} \frac{\left(-b\right) - \left(b - 2 \cdot \frac{c \cdot a}{b}\right)}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)} & \text{otherwise} \end{cases}} \leadsto \color{blue}{\begin{cases} \frac{c}{1 \cdot b} - \frac{b - \left(-b\right)}{2 \cdot a} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{(2 * \left(\frac{c}{b} \cdot a\right) + \left(\left(-b\right) - b\right))_*} & \text{otherwise} \end{cases}}\]
4.4
- Applied simplify to get
\[\begin{cases} \color{red}{\frac{c}{1 \cdot b} - \frac{b - \left(-b\right)}{2 \cdot a}} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{(2 * \left(\frac{c}{b} \cdot a\right) + \left(\left(-b\right) - b\right))_*} & \text{otherwise} \end{cases} \leadsto \begin{cases} \color{blue}{\frac{c}{b} - \frac{b - \left(-b\right)}{2 \cdot a}} & \text{when } b \ge 0 \\ \frac{2 \cdot c}{(2 * \left(\frac{c}{b} \cdot a\right) + \left(\left(-b\right) - b\right))_*} & \text{otherwise} \end{cases}\]
4.4
