Chapter 9.6, Problem 33P

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

$6t^2-96=0$

To determine

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

Answer to Problem 33P

The solution for the equation is $t=4$ and $t=-4$ .

Explanation of Solution

Given information :

The given equation is $6t^2-96=0$ .

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

  $6t^2-96=0$

  $a=6$ , $b=0$ and $c=-96$ .

Therefore,

  $\begin{array}{l}t=\frac{-\left(0\right)\pm \sqrt{{\left(0\right)}^2-4\left(6\right)\left(-96\right)}}{2\left(6\right)}\\ t=\frac{0\pm \sqrt{2304}}{12}\\ t=\pm \frac{48}{12}\\ t=\frac{48}{12}\text{ and }t=-\frac{48}{12}\\ t=4\text{ and }t=-4\end{array}$

Hence,

The solution for the equation is $t=4$ and $t=-4$ .