Initial program 52.6
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
- Using strategy
rm Applied flip-+52.6
\[\leadsto \frac{\color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}}}{3 \cdot a}\]
Applied associate-/l/52.6
\[\leadsto \color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{\left(3 \cdot a\right) \cdot \left(\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}\right)}}\]
Simplified0.5
\[\leadsto \frac{\color{blue}{3 \cdot \left(c \cdot a\right)}}{\left(3 \cdot a\right) \cdot \left(\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}\right)}\]
- Using strategy
rm Applied associate-/r*0.4
\[\leadsto \color{blue}{\frac{\frac{3 \cdot \left(c \cdot a\right)}{3 \cdot a}}{\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}}\]
Taylor expanded around inf 0.1
\[\leadsto \frac{\color{blue}{c}}{\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}\]
- Using strategy
rm Applied add-cbrt-cube0.2
\[\leadsto \frac{c}{\left(-b\right) - \sqrt{\color{blue}{\sqrt[3]{\left(\left(b \cdot b - \left(3 \cdot a\right) \cdot c\right) \cdot \left(b \cdot b - \left(3 \cdot a\right) \cdot c\right)\right) \cdot \left(b \cdot b - \left(3 \cdot a\right) \cdot c\right)}}}}\]
Final simplification0.2
\[\leadsto \frac{c}{\left(-b\right) - \sqrt{\sqrt[3]{\left(\left(b \cdot b - c \cdot \left(3 \cdot a\right)\right) \cdot \left(b \cdot b - c \cdot \left(3 \cdot a\right)\right)\right) \cdot \left(b \cdot b - c \cdot \left(3 \cdot a\right)\right)}}}\]
