Initial program 43.7
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
- Using strategy
rm Applied flip-+43.7
\[\leadsto \frac{\color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}}}{3 \cdot a}\]
Applied associate-/l/43.7
\[\leadsto \color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{\left(3 \cdot a\right) \cdot \left(\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}\right)}}\]
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 times-frac0.5
\[\leadsto \color{blue}{\frac{3}{3 \cdot a} \cdot \frac{c \cdot a}{\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}}\]
Simplified0.5
\[\leadsto \color{blue}{\frac{1}{a}} \cdot \frac{c \cdot a}{\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}\]
Simplified0.5
\[\leadsto \frac{1}{a} \cdot \color{blue}{\frac{c \cdot a}{\left(-b\right) - \sqrt{(-3 \cdot \left(c \cdot a\right) + \left(b \cdot b\right))_*}}}\]
- Using strategy
rm Applied frac-times0.4
\[\leadsto \color{blue}{\frac{1 \cdot \left(c \cdot a\right)}{a \cdot \left(\left(-b\right) - \sqrt{(-3 \cdot \left(c \cdot a\right) + \left(b \cdot b\right))_*}\right)}}\]
Simplified0.4
\[\leadsto \frac{\color{blue}{a \cdot c}}{a \cdot \left(\left(-b\right) - \sqrt{(-3 \cdot \left(c \cdot a\right) + \left(b \cdot b\right))_*}\right)}\]
Final simplification0.4
\[\leadsto \frac{a \cdot c}{a \cdot \left(\left(-b\right) - \sqrt{(-3 \cdot \left(a \cdot c\right) + \left(b \cdot b\right))_*}\right)}\]
