\(\frac{1}{2} \cdot \frac{\left(-b\right) + \sqrt{{b}^2 - a \cdot \left(c \cdot 4\right)}}{a}\)
- Started with
\[\frac{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
15.8
- Using strategy
rm 15.8
- Applied pow1 to get
\[\frac{\color{red}{\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a} \leadsto \frac{\color{blue}{{\left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}}{2 \cdot a}\]
15.8
- Using strategy
rm 15.8
- Applied *-un-lft-identity to get
\[\frac{{\color{red}{\left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}}^{1}}{2 \cdot a} \leadsto \frac{{\color{blue}{\left(1 \cdot \left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)\right)}}^{1}}{2 \cdot a}\]
15.8
- Applied unpow-prod-down to get
\[\frac{\color{red}{{\left(1 \cdot \left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)\right)}^{1}}}{2 \cdot a} \leadsto \frac{\color{blue}{{1}^{1} \cdot {\left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}}{2 \cdot a}\]
15.8
- Applied times-frac to get
\[\color{red}{\frac{{1}^{1} \cdot {\left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}{2 \cdot a}} \leadsto \color{blue}{\frac{{1}^{1}}{2} \cdot \frac{{\left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}{a}}\]
15.8
- Applied simplify to get
\[\color{red}{\frac{{1}^{1}}{2}} \cdot \frac{{\left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}{a} \leadsto \color{blue}{\frac{1}{2}} \cdot \frac{{\left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}{a}\]
15.8
- Applied simplify to get
\[\frac{1}{2} \cdot \color{red}{\frac{{\left(\left(-b\right) + \sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}^{1}}{a}} \leadsto \frac{1}{2} \cdot \color{blue}{\frac{\left(-b\right) + \sqrt{{b}^2 - a \cdot \left(c \cdot 4\right)}}{a}}\]
15.8
