Chapter 9, Problem 17PT

To determine

To solve equation by completing the square.

Answer to Problem 17PT

  $x=3,-6$

Explanation of Solution

Given information :

The function provided is $2x^2-36=-6x$

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 :

  $2x^2-36=-6x$

The above expression can also be written as.

  $x^2+3x-18=0$

Completing the sqaure.

  $x^2+3x+2.25=18+2.25$

Taking square root of both sides

  $\sqrt{{(x+1.5)}^2}=\sqrt{20.25}$

Simplifying.

  $x=\pm 4.5-1.5$

Therefore, $x=3,-6$ .