Initial program 28.6
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
- Using strategy
rm Applied flip-+28.6
\[\leadsto \frac{\color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}}}{3 \cdot a}\]
Applied associate-/l/28.6
\[\leadsto \color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{\left(3 \cdot a\right) \cdot \left(\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}\right)}}\]
Simplified0.6
\[\leadsto \frac{\color{blue}{3 \cdot \left(c \cdot a\right)}}{\left(3 \cdot a\right) \cdot \left(\left(-b\right) - \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}\right)}\]
- 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-lft-in0.6
\[\leadsto \frac{3 \cdot \left(c \cdot a\right)}{\color{blue}{\left(3 \cdot a\right) \cdot \left(-b\right) + \left(3 \cdot a\right) \cdot \left(-\sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}\right)}}\]
Simplified0.6
\[\leadsto \frac{3 \cdot \left(c \cdot a\right)}{\left(3 \cdot a\right) \cdot \left(-b\right) + \color{blue}{\sqrt{a \cdot \left(c \cdot -3\right) + b \cdot b} \cdot \left(-3 \cdot a\right)}}\]
- Using strategy
rm Applied flip3-+0.6
\[\leadsto \frac{3 \cdot \left(c \cdot a\right)}{\left(3 \cdot a\right) \cdot \left(-b\right) + \sqrt{\color{blue}{\frac{{\left(a \cdot \left(c \cdot -3\right)\right)}^{3} + {\left(b \cdot b\right)}^{3}}{\left(a \cdot \left(c \cdot -3\right)\right) \cdot \left(a \cdot \left(c \cdot -3\right)\right) + \left(\left(b \cdot b\right) \cdot \left(b \cdot b\right) - \left(a \cdot \left(c \cdot -3\right)\right) \cdot \left(b \cdot b\right)\right)}}} \cdot \left(-3 \cdot a\right)}\]
Applied sqrt-div0.6
\[\leadsto \frac{3 \cdot \left(c \cdot a\right)}{\left(3 \cdot a\right) \cdot \left(-b\right) + \color{blue}{\frac{\sqrt{{\left(a \cdot \left(c \cdot -3\right)\right)}^{3} + {\left(b \cdot b\right)}^{3}}}{\sqrt{\left(a \cdot \left(c \cdot -3\right)\right) \cdot \left(a \cdot \left(c \cdot -3\right)\right) + \left(\left(b \cdot b\right) \cdot \left(b \cdot b\right) - \left(a \cdot \left(c \cdot -3\right)\right) \cdot \left(b \cdot b\right)\right)}}} \cdot \left(-3 \cdot a\right)}\]
Applied associate-*l/0.6
\[\leadsto \frac{3 \cdot \left(c \cdot a\right)}{\left(3 \cdot a\right) \cdot \left(-b\right) + \color{blue}{\frac{\sqrt{{\left(a \cdot \left(c \cdot -3\right)\right)}^{3} + {\left(b \cdot b\right)}^{3}} \cdot \left(-3 \cdot a\right)}{\sqrt{\left(a \cdot \left(c \cdot -3\right)\right) \cdot \left(a \cdot \left(c \cdot -3\right)\right) + \left(\left(b \cdot b\right) \cdot \left(b \cdot b\right) - \left(a \cdot \left(c \cdot -3\right)\right) \cdot \left(b \cdot b\right)\right)}}}}\]
Final simplification0.6
\[\leadsto \frac{\left(a \cdot c\right) \cdot 3}{\left(a \cdot -3\right) \cdot b + \frac{\left(a \cdot -3\right) \cdot \sqrt{{\left(b \cdot b\right)}^{3} + {\left(a \cdot \left(c \cdot -3\right)\right)}^{3}}}{\sqrt{\left(\left(b \cdot b\right) \cdot \left(b \cdot b\right) - \left(a \cdot \left(c \cdot -3\right)\right) \cdot \left(b \cdot b\right)\right) + \left(a \cdot \left(c \cdot -3\right)\right) \cdot \left(a \cdot \left(c \cdot -3\right)\right)}}}\]
