Initial program 28.6
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
- Using strategy
rm Applied flip-+28.6
\[\leadsto \frac{\color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]
Applied simplify0.4
\[\leadsto \frac{\frac{\color{blue}{c \cdot \left(a \cdot 4\right)}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\]
- Using strategy
rm Applied add-cbrt-cube0.5
\[\leadsto \frac{\frac{c \cdot \left(a \cdot 4\right)}{\left(-b\right) - \sqrt{\color{blue}{\sqrt[3]{\left(\left(b \cdot b - \left(4 \cdot a\right) \cdot c\right) \cdot \left(b \cdot b - \left(4 \cdot a\right) \cdot c\right)\right) \cdot \left(b \cdot b - \left(4 \cdot a\right) \cdot c\right)}}}}}{2 \cdot a}\]
Applied simplify0.5
\[\leadsto \frac{\frac{c \cdot \left(a \cdot 4\right)}{\left(-b\right) - \sqrt{\sqrt[3]{\color{blue}{{\left(b \cdot b - 4 \cdot \left(a \cdot c\right)\right)}^{3}}}}}}{2 \cdot a}\]
Taylor expanded around 0 0.5
\[\leadsto \frac{\frac{c \cdot \left(a \cdot 4\right)}{\left(-b\right) - \sqrt{\sqrt[3]{{\color{blue}{\left({b}^{2} - 4 \cdot \left(c \cdot a\right)\right)}}^{3}}}}}{2 \cdot a}\]
Applied simplify0.3
\[\leadsto \color{blue}{\frac{\frac{\frac{c}{2}}{a} \cdot \left(4 \cdot a\right)}{\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot 4\right) \cdot a}}}\]
