Chapter 9.3, Problem 2BGP

To determine

To solve the given equation using graphing.

Answer to Problem 2BGP

The values of x is -4 .

Explanation of Solution

Given information :

The function provided is $x^2=-8x-16$ , or it can be written as $x^2+8x+16=0$ .

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 has x-intercept at $\left(-4,0\right)$ .

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

  $x^2+8x+16=0$

This is the given equation.

  $=>{\left(-4\right)}^2+8\left(-4\right)+16=0$

Putting $x=-4$

  $=>16-32+16=0$

Simplifying this

  $=>0=0$

Thus the test is a success and the result is -4 . Since the parabola has only one x-intercept, there would only one answer for x .