Initial program 43.8
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
Initial simplification43.8
\[\leadsto \frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{2 \cdot a}\]
- Using strategy
rm Applied flip--43.8
\[\leadsto \frac{\color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} \cdot \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b \cdot b}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} + b}}}{2 \cdot a}\]
Applied associate-/l/43.8
\[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} \cdot \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b \cdot b}{\left(2 \cdot a\right) \cdot \left(\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} + b\right)}}\]
Simplified0.4
\[\leadsto \frac{\color{blue}{\left(c \cdot -4\right) \cdot a}}{\left(2 \cdot a\right) \cdot \left(\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} + b\right)}\]
- Using strategy
rm Applied associate-/l*0.2
\[\leadsto \color{blue}{\frac{c \cdot -4}{\frac{\left(2 \cdot a\right) \cdot \left(\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} + b\right)}{a}}}\]
- Using strategy
rm Applied add-cbrt-cube0.3
\[\leadsto \frac{c \cdot -4}{\frac{\left(2 \cdot a\right) \cdot \left(\sqrt{\color{blue}{\sqrt[3]{\left(\left(b \cdot b - \left(c \cdot a\right) \cdot 4\right) \cdot \left(b \cdot b - \left(c \cdot a\right) \cdot 4\right)\right) \cdot \left(b \cdot b - \left(c \cdot a\right) \cdot 4\right)}}} + b\right)}{a}}\]
Final simplification0.3
\[\leadsto \frac{c \cdot -4}{\frac{\left(b + \sqrt{\sqrt[3]{\left(b \cdot b - 4 \cdot \left(a \cdot c\right)\right) \cdot \left(\left(b \cdot b - 4 \cdot \left(a \cdot c\right)\right) \cdot \left(b \cdot b - 4 \cdot \left(a \cdot c\right)\right)\right)}}\right) \cdot \left(2 \cdot a\right)}{a}}\]
