Initial program 28.6
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
Initial simplification28.6
\[\leadsto \frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{2 \cdot a}\]
- Using strategy
rm Applied flip--28.6
\[\leadsto \frac{\color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} \cdot \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b \cdot b}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} + b}}}{2 \cdot a}\]
Applied associate-/l/28.6
\[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} \cdot \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b \cdot b}{\left(2 \cdot a\right) \cdot \left(\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} + b\right)}}\]
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*0.3
\[\leadsto \color{blue}{\frac{c \cdot -4}{\frac{\left(2 \cdot a\right) \cdot \left(\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} + b\right)}{a}}}\]
- Using strategy
rm Applied *-un-lft-identity0.3
\[\leadsto \frac{c \cdot -4}{\color{blue}{1 \cdot \frac{\left(2 \cdot a\right) \cdot \left(\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} + b\right)}{a}}}\]
Applied associate-/r*0.3
\[\leadsto \color{blue}{\frac{\frac{c \cdot -4}{1}}{\frac{\left(2 \cdot a\right) \cdot \left(\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} + b\right)}{a}}}\]
Simplified0.3
\[\leadsto \frac{\frac{c \cdot -4}{1}}{\color{blue}{\left(\sqrt{a \cdot \left(c \cdot -4\right) + b \cdot b} + b\right) \cdot 2}}\]
Final simplification0.3
\[\leadsto \frac{c \cdot -4}{\left(b + \sqrt{b \cdot b + a \cdot \left(c \cdot -4\right)}\right) \cdot 2}\]
