Question

Which of the following is the solution set of x² + 8x + 12 = 0?

Answer 1

`\fbox{\begin{minipage}{9em}x = -2 and x = -6\end{minipage}}`

Explanation:

Given:

`x^(2) + 8x + 12 = 0`

Solve for:

`x`

Solution:

Step 1: Select the formula to solve for
`x`

There are some ways to solve quadratic equations.

One of the simple way (if possible) is performing the factorization.

Another way is using the quadratic formula.

Here, we are going to use factorization.

Step 2: Perform factorization

`x^(2) + 8x + 12 = 0`

<=>
`x^(2) + 2x + 6x + 12 = 0`

<=>
`(x^(2) + 2x) + (6x + 12) = 0`

<=>
`x(x + 2) + 6(x + 2) = 0`

<=>
`(x + 2)(x + 6) = 0`

<=>
`x = -2` or
`x = -6`

Hope this helps!

:)