## Precalculus (6th Edition) Blitzer

The value of the expression $\frac{-b-\sqrt{{{b}^{2}}-4ac}}{2a}$ for $a=2,b=9,\text{ and }c=-5$ is $-5$.
Consider the expression, $\frac{-b-\sqrt{{{b}^{2}}-4ac}}{2a}$ Now, substitute the value $a=2,b=9,\text{ and }c=-5$ in the expression $\frac{-b-\sqrt{{{b}^{2}}-4ac}}{2a}$ Therefore, \begin{align} & \frac{-b-\sqrt{{{b}^{2}}-4ac}}{2a}=\frac{-9-\sqrt{{{\left( 9 \right)}^{2}}-4\cdot 2\cdot \left( -5 \right)}}{2\cdot 2} \\ & =\frac{-9-\sqrt{81+40}}{4} \\ & =\frac{-9-\sqrt{121}}{4} \\ & =\frac{-9-11}{4} \end{align} Further simplify, \begin{align} & \frac{-b-\sqrt{{{b}^{2}}-4ac}}{2a}=\frac{-20}{4} \\ & =-5 \end{align} Therefore, the value of the expression $\frac{-b-\sqrt{{{b}^{2}}-4ac}}{2a}$ for $a=2,b=9,\text{ and }c=-5$ is $-5$.