Initial program 28.2
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
- Using strategy
rm Applied flip-+28.2
\[\leadsto \frac{\color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}}}{3 \cdot a}\]
Applied associate-/l/28.2
\[\leadsto \color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{\left(3 \cdot a\right) \cdot \left(\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}\right)}}\]
Simplified0.6
\[\leadsto \frac{\color{blue}{3 \cdot \left(c \cdot a\right)}}{\left(3 \cdot a\right) \cdot \left(\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}\right)}\]
- Using strategy
rm Applied flip--0.6
\[\leadsto \frac{3 \cdot \left(c \cdot a\right)}{\left(3 \cdot a\right) \cdot \left(\left(-b\right) - \sqrt{\color{blue}{\frac{\left(b \cdot b\right) \cdot \left(b \cdot b\right) - \left(\left(3 \cdot a\right) \cdot c\right) \cdot \left(\left(3 \cdot a\right) \cdot c\right)}{b \cdot b + \left(3 \cdot a\right) \cdot c}}}\right)}\]
- Using strategy
rm Applied sub-neg0.6
\[\leadsto \frac{3 \cdot \left(c \cdot a\right)}{\left(3 \cdot a\right) \cdot \color{blue}{\left(\left(-b\right) + \left(-\sqrt{\frac{\left(b \cdot b\right) \cdot \left(b \cdot b\right) - \left(\left(3 \cdot a\right) \cdot c\right) \cdot \left(\left(3 \cdot a\right) \cdot c\right)}{b \cdot b + \left(3 \cdot a\right) \cdot c}}\right)\right)}}\]
Applied distribute-lft-in0.6
\[\leadsto \frac{3 \cdot \left(c \cdot a\right)}{\color{blue}{\left(3 \cdot a\right) \cdot \left(-b\right) + \left(3 \cdot a\right) \cdot \left(-\sqrt{\frac{\left(b \cdot b\right) \cdot \left(b \cdot b\right) - \left(\left(3 \cdot a\right) \cdot c\right) \cdot \left(\left(3 \cdot a\right) \cdot c\right)}{b \cdot b + \left(3 \cdot a\right) \cdot c}}\right)}}\]
Simplified0.6
\[\leadsto \frac{3 \cdot \left(c \cdot a\right)}{\left(3 \cdot a\right) \cdot \left(-b\right) + \color{blue}{\left(-3 \cdot a\right) \cdot \sqrt{\frac{(\left(c \cdot a\right) \cdot -3 + \left(b \cdot b\right))_*}{1}}}}\]
Final simplification0.6
\[\leadsto \frac{\left(a \cdot c\right) \cdot 3}{b \cdot \left(a \cdot -3\right) + \sqrt{(\left(a \cdot c\right) \cdot -3 + \left(b \cdot b\right))_*} \cdot \left(a \cdot -3\right)}\]
