\(\frac{1}{(\left(\frac{1}{c}\right) * \left(\sqrt{{b/2}^2 - c \cdot a}\right) + \left(-\frac{b/2}{c}\right))_*}\)
- Started with
\[\frac{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}{a}\]
15.8
- Using strategy
rm 15.8
- Applied flip-- to get
\[\frac{\color{red}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\color{blue}{\frac{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}}{a}\]
20.7
- Applied simplify to get
\[\frac{\frac{\color{red}{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\frac{\color{blue}{a \cdot c}}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}{a}\]
14.5
- Using strategy
rm 14.5
- Applied add-exp-log to get
\[\frac{\frac{a \cdot c}{\left(-b/2\right) + \color{red}{\sqrt{{b/2}^2 - a \cdot c}}}}{a} \leadsto \frac{\frac{a \cdot c}{\left(-b/2\right) + \color{blue}{e^{\log \left(\sqrt{{b/2}^2 - a \cdot c}\right)}}}}{a}\]
15.3
- Using strategy
rm 15.3
- Applied clear-num to get
\[\color{red}{\frac{\frac{a \cdot c}{\left(-b/2\right) + e^{\log \left(\sqrt{{b/2}^2 - a \cdot c}\right)}}}{a}} \leadsto \color{blue}{\frac{1}{\frac{a}{\frac{a \cdot c}{\left(-b/2\right) + e^{\log \left(\sqrt{{b/2}^2 - a \cdot c}\right)}}}}}\]
15.3
- Applied simplify to get
\[\frac{1}{\color{red}{\frac{a}{\frac{a \cdot c}{\left(-b/2\right) + e^{\log \left(\sqrt{{b/2}^2 - a \cdot c}\right)}}}}} \leadsto \frac{1}{\color{blue}{(\left(\frac{1}{c}\right) * \left(\sqrt{b/2 \cdot b/2 - c \cdot a}\right) + \left(-\frac{b/2}{c}\right))_*}}\]
13.7
- Applied simplify to get
\[\frac{1}{(\left(\frac{1}{c}\right) * \color{red}{\left(\sqrt{b/2 \cdot b/2 - c \cdot a}\right)} + \left(-\frac{b/2}{c}\right))_*} \leadsto \frac{1}{(\left(\frac{1}{c}\right) * \color{blue}{\left(\sqrt{{b/2}^2 - c \cdot a}\right)} + \left(-\frac{b/2}{c}\right))_*}\]
13.7
