Chapter 4.2, Problem 24PPS

To determine

To solve: the given equation. If exact roots cannot be found, state the consecutive integers between which the roots are located.

Answer to Problem 24PPS

  $x=9$ .

Explanation of Solution

Given:

The given equation is $x^2-18x=-81$ .

Calculation:

The given equation is expressed as $x^2-18x+81=0$ .

Now, solve the given equation by factor method. Therefore,

  $\begin{array}{l}{x}^2-18x+81=0\left\{\text{given function}\right\}\\ x^2-9x-9x-81=0\{arrangethe\text{factor}}\\ x\left(x-9\right)-9\left(x-9\right)=0\{arrangethe\text{factor}}\\ \left(x-9\right)\left(x-9\right)=0\{\text{factor}}\end{array}$

Therefore, $\left(x-9\right)=0\Rightarrow x=9$

Thus, the zeros of the function are $x=9,x=9$ .

Hence, the solution of the given equation is $x=9$ .