Initial program 52.5
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
Initial simplification52.5
\[\leadsto \frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{2 \cdot a}\]
- Using strategy
rm Applied flip--52.5
\[\leadsto \frac{\color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} \cdot \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b \cdot b}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} + b}}}{2 \cdot a}\]
Applied associate-/l/52.5
\[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} \cdot \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b \cdot b}{\left(2 \cdot a\right) \cdot \left(\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} + b\right)}}\]
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-/r*0.2
\[\leadsto \color{blue}{\frac{\frac{\left(c \cdot -4\right) \cdot a}{2 \cdot a}}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} + b}}\]
- Using strategy
rm Applied flip3--0.2
\[\leadsto \frac{\frac{\left(c \cdot -4\right) \cdot a}{2 \cdot a}}{\sqrt{\color{blue}{\frac{{\left(b \cdot b\right)}^{3} - {\left(\left(c \cdot a\right) \cdot 4\right)}^{3}}{\left(b \cdot b\right) \cdot \left(b \cdot b\right) + \left(\left(\left(c \cdot a\right) \cdot 4\right) \cdot \left(\left(c \cdot a\right) \cdot 4\right) + \left(b \cdot b\right) \cdot \left(\left(c \cdot a\right) \cdot 4\right)\right)}}} + b}\]
Final simplification0.2
\[\leadsto \frac{\frac{\left(c \cdot -4\right) \cdot a}{a \cdot 2}}{b + \sqrt{\frac{{\left(b \cdot b\right)}^{3} - {\left(4 \cdot \left(a \cdot c\right)\right)}^{3}}{\left(b \cdot b\right) \cdot \left(b \cdot b\right) + \left(\left(4 \cdot \left(a \cdot c\right)\right) \cdot \left(b \cdot b\right) + \left(4 \cdot \left(a \cdot c\right)\right) \cdot \left(4 \cdot \left(a \cdot c\right)\right)\right)}}}\]
