Initial program 44.1
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
Initial simplification44.1
\[\leadsto \frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{2 \cdot a}\]
- Using strategy
rm Applied flip--44.1
\[\leadsto \frac{\color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} \cdot \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b \cdot b}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} + b}}}{2 \cdot a}\]
Applied associate-/l/44.1
\[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} \cdot \sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b \cdot b}{\left(2 \cdot a\right) \cdot \left(\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} + b\right)}}\]
Simplified0.4
\[\leadsto \frac{\color{blue}{\left(c \cdot -4\right) \cdot a}}{\left(2 \cdot a\right) \cdot \left(\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} + b\right)}\]
- Using strategy
rm Applied times-frac0.4
\[\leadsto \color{blue}{\frac{c \cdot -4}{2 \cdot a} \cdot \frac{a}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} + b}}\]
Simplified0.4
\[\leadsto \color{blue}{\frac{\frac{c}{\frac{-1}{2}}}{a}} \cdot \frac{a}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} + b}\]
- Using strategy
rm Applied pow10.4
\[\leadsto \frac{\frac{c}{\frac{-1}{2}}}{a} \cdot \color{blue}{{\left(\frac{a}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} + b}\right)}^{1}}\]
Applied pow10.4
\[\leadsto \color{blue}{{\left(\frac{\frac{c}{\frac{-1}{2}}}{a}\right)}^{1}} \cdot {\left(\frac{a}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} + b}\right)}^{1}\]
Applied pow-prod-down0.4
\[\leadsto \color{blue}{{\left(\frac{\frac{c}{\frac{-1}{2}}}{a} \cdot \frac{a}{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} + b}\right)}^{1}}\]
Simplified0.2
\[\leadsto {\color{blue}{\left(\frac{c \cdot -2}{\sqrt{\left(c \cdot -4\right) \cdot a + b \cdot b} + b}\right)}}^{1}\]
Final simplification0.2
\[\leadsto \frac{c \cdot -2}{b + \sqrt{b \cdot b + \left(-4 \cdot c\right) \cdot a}}\]
