Chapter 8.3, Problem 7CYU

To determine

To find:The solution of given equation.

Answer to Problem 7CYU

The solution of given equation is $x=9,6$ .

Explanation of Solution

Given information:The expression is $x^2-15x+54=0$

Calculation:

Consider the equation.

  $x^2-15x+54=0$

The solution of the equation is,

  $\begin{array}{c}{x}^2-15x+54=0\\ x^2-9x-6x+54=0\\ x\left(x-9\right)-6\left(x-9\right)=0\\ \left(x-9\right)\left(x-6\right)=0\\ x=9,6\end{array}$

Substitute $x=9$ in above equation.

  $\begin{array}{l}{\left(9\right)}^2-15\left(9\right)+54=0\\ 81-135+54=0\\ 0=0\end{array}$

Substitute $x=6$ in above equation.

  $\begin{array}{l}{\left(6\right)}^2-15\left(6\right)+54=0\\ 36-90+54=0\\ 0=0\end{array}$