Chapter 9, Problem 12PT

To determine

To solve equation by factoring.

Answer to Problem 12PT

  $x=-9$

Explanation of Solution

Given information :

The function provided is $x^2+18x+81=0$

Formula used :

For some of the equations the solution can be found by factoring. If the factored form of a quadratic equation has real numbers, it will have roots.

  $(x-h)(x-k)=0$

In the factored form it is assumed that at least one of the factors is equal to 0. Therefore, if product if two factors is 0 then at least one of the factors must be zero, this is known as the Zero Product Property

Either,

  $(x-h)=0$

Or,

  $(x-k)=0$

Calculation :

  $x^2+18x+81=0$

The above expression can also be written as.

  $x^2+9x+9x+81$

In factored form.

  $(x+9)(x+9)=0$

Simplifying.

  ${(x+9)}^2=0$

The above expression can be solved to get $x=-9$

We get only one root $x=-9$ as $x^2+18x+81=0$ is a perfect square.