Chapter 9, Problem 11PT

To determine

To solve equation by graphing

Answer to Problem 11PT

  $x=-4.2,1.2$

Explanation of Solution

Given information :

The function provided is $x^2-5=-3x$

Graph :

  

Interpretation :

To solve the equation using graphing method, the equation is rewritten in standard form and the related function $f(x)=a{x}^2+bx+c$ is graphed. The x- intercepts need to be identified from the graph and verified by substituting the corresponding values of x in the equation.

Here, since the first intercept is between $(-5,0)$ and $(-4,0)$ and the second intercept is between $(1,0)$ and $(2,0)$ . We will have to estimate the solution.

All values between the pair of points are taken with an increment of 0.1. The value closest to 0 is considered from the values in the table.

  $x^2+3x-5=0$

For intercept between $(-5,0)$ and $(-4,0)$ .

x	y
-4.9	4.31
-4.8	3.64
-4.7	2.99
-4.6	2.36
-4.5	1.75
-4.4	1.16
-4.3	0.59
-4.2	0.04
-4.1	-0.49

Therefore, $x=-4.2$ is taken as the approximate solution for the given equation as the value corresponding is the closest to 0.

For intercept between $(1,0)$ and $(2,0)$

x	y
1.1	-0.49
1.2	0.04
1.3	0.59

Therefore, $x=1.2$ is taken as the approximate solution for the given equation as the value corresponding is the closest to 0.