Initial program 28.2
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
Applied simplify28.2
\[\leadsto \color{blue}{\frac{\sqrt{(\left(4 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} - b}{2 \cdot a}}\]
- Using strategy
rm Applied flip--28.2
\[\leadsto \frac{\color{blue}{\frac{\sqrt{(\left(4 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} \cdot \sqrt{(\left(4 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} - b \cdot b}{\sqrt{(\left(4 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} + b}}}{2 \cdot a}\]
Applied simplify0.4
\[\leadsto \frac{\frac{\color{blue}{\left(c \cdot a\right) \cdot \left(-4\right)}}{\sqrt{(\left(4 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} + b}}{2 \cdot a}\]
- Using strategy
rm Applied clear-num0.5
\[\leadsto \frac{\color{blue}{\frac{1}{\frac{\sqrt{(\left(4 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} + b}{\left(c \cdot a\right) \cdot \left(-4\right)}}}}{2 \cdot a}\]
- Using strategy
rm Applied *-un-lft-identity0.5
\[\leadsto \frac{\color{blue}{1 \cdot \frac{1}{\frac{\sqrt{(\left(4 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} + b}{\left(c \cdot a\right) \cdot \left(-4\right)}}}}{2 \cdot a}\]
Applied times-frac0.5
\[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{\frac{1}{\frac{\sqrt{(\left(4 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} + b}{\left(c \cdot a\right) \cdot \left(-4\right)}}}{a}}\]
Applied simplify0.4
\[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{\left(a \cdot 4\right) \cdot \left(-c\right)}{(a \cdot \left(\sqrt{(\left(a \cdot 4\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*}\right) + \left(a \cdot b\right))_*}}\]
