Chapter 9.5, Problem 24P

Solve each equation by completing the square. If necessary, round to the nearest hundredth.

$9x^2-42x+49=0$

To determine

To solve : the equation by completing the square

Answer to Problem 24P

The solution of the equation is $x=\frac{7}{3}$

Explanation of Solution

Given information :

The equation is

  $9x^2-42x+49=0$

Calculation :

The solution of the equation is

  $\begin{array}{l}9x^2-42x+49=0\\ x^2-\frac{42}{9}x+\frac{49}{9}=0\\ x^2-\frac{14}{3}x+\frac{49}{9}=0\\ x^2-2\cdot x\cdot \frac{7}{3}+{\left(\frac{7}{3}\right)}^2=0\\ {\left(x-\frac{7}{3}\right)}^2=0\\ x-\frac{7}{3}=0\\ x=\frac{7}{3}\end{array}$

Hence, the solution of the equation is $x=\frac{7}{3}$ .