Chapter 9.3, Problem 22PPS

To determine

To solve the given equation using graphing.

Answer to Problem 22PPS

The values of x are -1 and 2 .

Explanation of Solution

Given information :

The function provided is $3x^2-6=3x$ . This can be written as $3x^2-3x-6=0$

Formula used :

The given equation would be graphed as a function and the points of x-intercepts would be the results. For these points, the x-coordinate shall serve the purpose of the results.

To cross check, put these values in the given equation to confirm that the left-hand side and right-hand side matches.

Calculation :

The graph of the given equation is

In this, the parabola x-intercepts at $\left(-1,0\right)$ and $\left(2,0\right)$ .

Now, cross check by putting these values of x-coordinate in the given equation.

  $3x^2-3x-6=0$

This is the given equation.

  $=>3{\left(-1\right)}^2-3\left(-1\right)-6=0$

Putting $x=-1$

  $=>3+3-6=0$

Simplifying this

  $=>0=0$

Now, put the other result.

  $=>3{\left(2\right)}^2-3\left(2\right)-6=0$

Putting $x=2$

  $=>12-6-6=0$

Simplifying this

  $=>0=0$

Thus the test is a success and the result is -1 and 2 .