Chapter 9.6, Problem 1P

Use the quadratic formula to solve each equation.

$7c^2+8c+1=0$

To determine

To solve : The quadratic equation using quadratic formula.

Answer to Problem 1P

The solution for the equation is $c=-\frac{1}{7}$ and $c=-1$ .

Explanation of Solution

Given information :

The given equation is $7c^2+8c+1=0$ .

Calculation :

For the quadratic equation $a{x}^2+bx+c=0$ the quadratic formula is

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Now, for the given equation $7c^2+8c+1=0$

  $a=7$ , $b=8$ and $c=1$ .

Therefore,

  $\begin{array}{l}c=\frac{-8\pm \sqrt{8^2-4\left(7\right)\left(1\right)}}{2\left(7\right)}\\ c=\frac{-8\pm \sqrt{64-28}}{14}\\ c=\frac{-8\pm \sqrt{36}}{14}\\ c=\frac{-8\pm 6}{14}\\ c=\frac{-8+6}{14}\text{ and }c=\frac{-8-6}{14}\\ c=\frac{-2}{14}\text{ and }c=\frac{-14}{14}\\ c=-\frac{1}{7}\text{ and }c=-1\end{array}$

Hence,

The solution for the equation is $c=-\frac{1}{7}$ and $c=-1$ .