if b < -2.6747491353258983e+90 or -1.6249307588497366e-76 < b < -1.0745984396746834e-89

1. Started with
   \[\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   58.5
2. Applied taylor to get
   \[\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \leadsto \frac{-2 \cdot \frac{c \cdot a}{b}}{2 \cdot a}\]
   16.2
3. Taylor expanded around -inf to get
   \[\frac{\color{red}{-2 \cdot \frac{c \cdot a}{b}}}{2 \cdot a} \leadsto \frac{\color{blue}{-2 \cdot \frac{c \cdot a}{b}}}{2 \cdot a}\]
   16.2
4. Applied simplify to get
   \[\color{red}{\frac{-2 \cdot \frac{c \cdot a}{b}}{2 \cdot a}} \leadsto \color{blue}{\frac{c}{b} \cdot \frac{-2}{2}}\]
   0

if -2.6747491353258983e+90 < b < -1.6249307588497366e-76

1. Started with
   \[\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   43.9
2. Using strategy rm
   43.9
3. Applied flip-- to get
   \[\frac{\color{red}{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a} \leadsto \frac{\color{blue}{\frac{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}^2}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]
   43.9
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b\right)}^2 - {\left(\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}\right)}^2}}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a} \leadsto \frac{\frac{\color{blue}{c \cdot \left(4 \cdot a\right)}}{\left(-b\right) + \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]
   14.1

if -1.0745984396746834e-89 < b < 3.741572576046744e+123

1. Started with
   \[\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   11.7
2. Using strategy rm
   11.7
3. Applied div-sub to get
   \[\color{red}{\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}} \leadsto \color{blue}{\frac{-b}{2 \cdot a} - \frac{\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\]
   11.7

if 3.741572576046744e+123 < b

1. Started with
   \[\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   51.0
2. Using strategy rm
   51.0
3. Applied div-sub to get
   \[\color{red}{\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}} \leadsto \color{blue}{\frac{-b}{2 \cdot a} - \frac{\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\]
   51.0
4. Applied taylor to get
   \[\frac{-b}{2 \cdot a} - \frac{\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a} \leadsto \frac{-b}{2 \cdot a} - \frac{b - 2 \cdot \frac{c \cdot a}{b}}{2 \cdot a}\]
   12.7
5. Taylor expanded around inf to get
   \[\frac{-b}{2 \cdot a} - \frac{\color{red}{b - 2 \cdot \frac{c \cdot a}{b}}}{2 \cdot a} \leadsto \frac{-b}{2 \cdot a} - \frac{\color{blue}{b - 2 \cdot \frac{c \cdot a}{b}}}{2 \cdot a}\]
   12.7
6. Applied simplify to get
   \[\color{red}{\frac{-b}{2 \cdot a} - \frac{b - 2 \cdot \frac{c \cdot a}{b}}{2 \cdot a}} \leadsto \color{blue}{\left(\frac{\frac{c}{b}}{1} + \frac{-b}{2 \cdot a}\right) - \frac{\frac{b}{2}}{a}}\]
   0.0
7. Applied simplify to get
   \[\color{red}{\left(\frac{\frac{c}{b}}{1} + \frac{-b}{2 \cdot a}\right)} - \frac{\frac{b}{2}}{a} \leadsto \color{blue}{\left(\frac{c}{b} + \frac{-b}{2 \cdot a}\right)} - \frac{\frac{b}{2}}{a}\]
   0.0