Chapter SH, Problem 9.21EP

To determine

To solve equation by completing the square.

Answer to Problem 9.21EP

  $x=1.8,-3.4$

Explanation of Solution

Given information :

The function provided is $3x^2+5x=18$

Formula used :

To solve the equation by completing the square the $x^2$ and $x$ terms need to be isolated then the square is completed by adding the required constant to both sides of the equation.

Calculation :

  $3x^2+5x=18$

The above expression when divided by 3 on both sides can be written as.

  $x^2+\frac{5}{3}x+\frac{25}{36}=6+\frac{25}{36}$

Completing the sqaure.

  ${(x+\frac{5}{6})}^2=\frac{241}{36}$

Taking square root of both sides

  $x+0.83=\sqrt{6.69}$

Simplifying.

  $x=\pm 2.58-0.83$

Therefore, $x=1.756,-3.41$ .