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 sub-neg0.6
\[\leadsto \frac{3 \cdot \left(c \cdot a\right)}{\left(3 \cdot a\right) \cdot \color{blue}{\left(\left(-b\right) + \left(-\sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}\right)\right)}}\]
Applied distribute-rgt-in0.6
\[\leadsto \frac{3 \cdot \left(c \cdot a\right)}{\color{blue}{\left(-b\right) \cdot \left(3 \cdot a\right) + \left(-\sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}\right) \cdot \left(3 \cdot a\right)}}\]
Simplified0.6
\[\leadsto \frac{3 \cdot \left(c \cdot a\right)}{\left(-b\right) \cdot \left(3 \cdot a\right) + \color{blue}{\sqrt{b \cdot b - a \cdot \left(3 \cdot c\right)} \cdot \left(a \cdot -3\right)}}\]
- Using strategy
rm Applied *-un-lft-identity0.6
\[\leadsto \frac{3 \cdot \left(c \cdot a\right)}{\color{blue}{1 \cdot \left(\left(-b\right) \cdot \left(3 \cdot a\right) + \sqrt{b \cdot b - a \cdot \left(3 \cdot c\right)} \cdot \left(a \cdot -3\right)\right)}}\]
Applied times-frac0.6
\[\leadsto \color{blue}{\frac{3}{1} \cdot \frac{c \cdot a}{\left(-b\right) \cdot \left(3 \cdot a\right) + \sqrt{b \cdot b - a \cdot \left(3 \cdot c\right)} \cdot \left(a \cdot -3\right)}}\]
Simplified0.6
\[\leadsto \color{blue}{3} \cdot \frac{c \cdot a}{\left(-b\right) \cdot \left(3 \cdot a\right) + \sqrt{b \cdot b - a \cdot \left(3 \cdot c\right)} \cdot \left(a \cdot -3\right)}\]
Simplified0.5
\[\leadsto 3 \cdot \color{blue}{\frac{\frac{c}{-3}}{b + \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 3}}}\]
- Using strategy
rm Applied div-inv0.5
\[\leadsto 3 \cdot \color{blue}{\left(\frac{c}{-3} \cdot \frac{1}{b + \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 3}}\right)}\]
Applied associate-*r*0.5
\[\leadsto \color{blue}{\left(3 \cdot \frac{c}{-3}\right) \cdot \frac{1}{b + \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 3}}}\]
Final simplification0.5
\[\leadsto \frac{1}{\sqrt{b \cdot b - \left(a \cdot c\right) \cdot 3} + b} \cdot \left(\frac{c}{-3} \cdot 3\right)\]
