Initial program 28.9
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
Applied simplify28.9
\[\leadsto \color{blue}{\frac{\sqrt{(\left(3 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} - b}{3 \cdot a}}\]
- Using strategy
rm Applied flip--28.9
\[\leadsto \frac{\color{blue}{\frac{\sqrt{(\left(3 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} \cdot \sqrt{(\left(3 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} - b \cdot b}{\sqrt{(\left(3 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} + b}}}{3 \cdot a}\]
Applied simplify27.9
\[\leadsto \frac{\frac{\color{blue}{(\left(a \cdot 3\right) \cdot \left(-c\right) + \left(b \cdot b\right))_* - b \cdot b}}{\sqrt{(\left(3 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} + b}}{3 \cdot a}\]
Taylor expanded around 0 0.6
\[\leadsto \frac{\frac{\color{blue}{-3 \cdot \left(c \cdot a\right)}}{\sqrt{(\left(3 \cdot a\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} + b}}{3 \cdot a}\]
Applied simplify0.5
\[\leadsto \color{blue}{\frac{\frac{1}{3} \cdot \left(c \cdot -3\right)}{\sqrt{(\left(a \cdot 3\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} + b}}\]
- Using strategy
rm Applied pow10.5
\[\leadsto \frac{\frac{1}{3} \cdot \color{blue}{{\left(c \cdot -3\right)}^{1}}}{\sqrt{(\left(a \cdot 3\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} + b}\]
Applied pow10.5
\[\leadsto \frac{\color{blue}{{\left(\frac{1}{3}\right)}^{1}} \cdot {\left(c \cdot -3\right)}^{1}}{\sqrt{(\left(a \cdot 3\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} + b}\]
Applied pow-prod-down0.5
\[\leadsto \frac{\color{blue}{{\left(\frac{1}{3} \cdot \left(c \cdot -3\right)\right)}^{1}}}{\sqrt{(\left(a \cdot 3\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} + b}\]
Applied simplify0.4
\[\leadsto \frac{{\color{blue}{\left(\frac{-3 \cdot c}{3}\right)}}^{1}}{\sqrt{(\left(a \cdot 3\right) \cdot \left(-c\right) + \left(b \cdot b\right))_*} + b}\]
