Chapter 9.6, Problem 35P

Use any method to solve each equation. If necessary, round answers to the nearest hundredth.

$-g^2+4g+3=0$

To determine

To solve : The quadratic equation using any method and if necessary round answer to the nearest hundredth.

Answer to Problem 35P

The solution for the equation is $g=-0.65$ and $g=4.65$ .

Explanation of Solution

Given information :

The given equation is $-g^2+4g+3=0$ .

Calculation :

Use quadratic formula to solve the equation, 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

  $-g^2+4g+3=0$

  $a=-1$ , $b=4$ and $c=3$ .

Therefore,

  $\begin{array}{l}g=\frac{-4\pm \sqrt{{\left(4\right)}^2-4\left(-1\right)\left(3\right)}}{2\left(-1\right)}\\ g=\frac{-4\pm \sqrt{16+12}}{-2}\\ g=\frac{-4\pm \sqrt{28}}{-2}\\ g=\frac{-4\pm 2\sqrt{7}}{-2}\\ g=2\mp \sqrt{7}\\ g=2-\sqrt{7}\text{ and }g=2+\sqrt{7}\\ g=-0.65\text{ and }g=4.65\end{array}$

Hence,

The solution for the equation is $g=-0.65$ and $g=4.65$ .