Initial program 28.7
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
Applied simplify28.7
\[\leadsto \color{blue}{\frac{\sqrt{(\left(4 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} - b}{2 \cdot a}}\]
- Using strategy
rm Applied flip--28.7
\[\leadsto \frac{\color{blue}{\frac{\sqrt{(\left(4 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} \cdot \sqrt{(\left(4 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} - b \cdot b}{\sqrt{(\left(4 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} + b}}}{2 \cdot a}\]
Applied simplify0.5
\[\leadsto \frac{\frac{\color{blue}{\left(-c\right) \cdot \left(4 \cdot a\right)}}{\sqrt{(\left(4 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} + b}}{2 \cdot a}\]
- Using strategy
rm Applied *-un-lft-identity0.5
\[\leadsto \frac{\frac{\left(-c\right) \cdot \left(4 \cdot a\right)}{\color{blue}{1 \cdot \left(\sqrt{(\left(4 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} + b\right)}}}{2 \cdot a}\]
Applied times-frac0.4
\[\leadsto \frac{\color{blue}{\frac{-c}{1} \cdot \frac{4 \cdot a}{\sqrt{(\left(4 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} + b}}}{2 \cdot a}\]
Applied times-frac0.5
\[\leadsto \color{blue}{\frac{\frac{-c}{1}}{2} \cdot \frac{\frac{4 \cdot a}{\sqrt{(\left(4 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} + b}}{a}}\]
Applied simplify0.5
\[\leadsto \color{blue}{\left(-\frac{c}{2}\right)} \cdot \frac{\frac{4 \cdot a}{\sqrt{(\left(4 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} + b}}{a}\]
Applied simplify0.4
\[\leadsto \left(-\frac{c}{2}\right) \cdot \color{blue}{\frac{4}{b + \sqrt{(\left(-c\right) \cdot \left(4 \cdot a\right) + \left(b \cdot b\right))_*}}}\]
