Chapter 9, Problem 28SGR

To determine

To solve the given equation using graphing.

Answer to Problem 28SGR

The roots of x are 3 and 7 .

Explanation of Solution

Given information :

The function provided is $x^2-10x=-21$ . This can be written as $x^2-10x+21=0$ .

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.

If the roots are not on points that are integers, use the approximation method to compute the roots.

Else, put the x-intercept value in the equation. If the left-hand and right-hand sides of the equations match, it is a success and those will be the values of x.

Calculation :

The graph of the given equation is

  

The zeroes in the graph are at $\left(3,0\right)$ and $\left(7,0\right)$ .

Put these values in the given equation to recheck.

  ${\left(3\right)}^2-10\left(3\right)+21=0$

Putting $x=3$ in the given equation.

  $=>9-30+21=0$

Simplifying

  $=>30-30=0$

Hence first value of x is a success.

  ${\left(7\right)}^2-10\left(7\right)+21=0$

Putting $x=7$ in the given equation.

  $=>49-70+21=0$

Simplifying

  $=>70-70=0$

Hence second value of x is a success.