Question

Solve each equation by completing the square

n2 + 4n - 12 - 0

Answer 1

`n=-6\\n=2`

Explanation:

We begin with the equation
`n^2+4n-12=0`

When we complete the square, we work off the the second coefficient. In this case, it is 4.

The first thing we must do is half this number

This gives us 2.

Then we have to square it, which gives us 4.

We then can add and subtract this number from this equation

`n^2+4n+4-12-4=0`

This doesn't look like much, but we can now group these terms together and then solve the problem.

`(n^2+4n+4)-12-4=0\\\\(n^2+4n+4)-16=0\\\\n^2+4n+4=16\\\\(n+2)^2=16\\\\(n+2)^2=4^2\\\\\±4=n+2\\\\n=-6\\n=2`