Chapter SH, Problem 9.18EP

To determine

To solve equation by completing the square.

Answer to Problem 9.18EP

  $x=-3,-2$

Explanation of Solution

Given information :

The function provided is $x^2+5x+6=0$

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 :

  $x^2+5x+6=0$

The above expression can also be written as.

  $x^2+5x+6.25=-6+6.25$

Completing the sqaure.

  ${(x+2.5)}^2=0.25$

Taking square root of both sides

  $x+2.5=\sqrt{0.25}$

Simplifying.

  $x=\pm 0.5-2.5$

Therefore, $x=-3,-2$ .