Initial program 1.7
\[\frac{\left(\frac{\left(-b_2\right)}{\left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)}\right)}{a}\]
Simplified1.7
\[\leadsto \color{blue}{\frac{\left(\left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(c \cdot a\right)\right)}\right) - b_2\right)}{a}}\]
- Using strategy
rm Applied p16-flip--2.7
\[\leadsto \frac{\left(\left(\sqrt{\color{blue}{\left(\frac{\left(\left(\left(b_2 \cdot b_2\right) \cdot \left(b_2 \cdot b_2\right)\right) - \left(\left(c \cdot a\right) \cdot \left(c \cdot a\right)\right)\right)}{\left(\frac{\left(b_2 \cdot b_2\right)}{\left(c \cdot a\right)}\right)}\right)}}\right) - b_2\right)}{a}\]
- Using strategy
rm Applied difference-of-squares2.6
\[\leadsto \frac{\left(\left(\sqrt{\left(\frac{\color{blue}{\left(\left(\frac{\left(b_2 \cdot b_2\right)}{\left(c \cdot a\right)}\right) \cdot \left(\left(b_2 \cdot b_2\right) - \left(c \cdot a\right)\right)\right)}}{\left(\frac{\left(b_2 \cdot b_2\right)}{\left(c \cdot a\right)}\right)}\right)}\right) - b_2\right)}{a}\]
Applied associate-/l*1.7
\[\leadsto \frac{\left(\left(\sqrt{\color{blue}{\left(\frac{\left(\frac{\left(b_2 \cdot b_2\right)}{\left(c \cdot a\right)}\right)}{\left(\frac{\left(\frac{\left(b_2 \cdot b_2\right)}{\left(c \cdot a\right)}\right)}{\left(\left(b_2 \cdot b_2\right) - \left(c \cdot a\right)\right)}\right)}\right)}}\right) - b_2\right)}{a}\]
Final simplification1.7
\[\leadsto \frac{\sqrt{\frac{b_2 \cdot b_2 + c \cdot a}{\frac{b_2 \cdot b_2 + c \cdot a}{b_2 \cdot b_2 - c \cdot a}}} - b_2}{a}\]
