Question

Solve each equation by completing the square 6n^2+12n-45= 3There is a mistake somewhere in my process and I can’t figure out where. Hope someone can help me.

Answer 1

Answer:

n = 2, -4

Step-by-step explanation:

Given:

`6n^2+12n-45=3`

Add 45 to both sides:

`\begin{gathered} 6n^2+12n=3+45 \\ \\ 6n^2+12n=48 \end{gathered}`

Divide both sides by 6

`n^2+2n=8`

Note that:

`(n+1)^2=n^2+2n+1`

We can simple use this and subtract 1 from the expression as the extra value

`(n+1)^2-1=8`

Add 1 to both sides

`(n+1)^2=9`

Take square roots of both sides

`\begin{gathered} n+1=\pm√(9) \\ \\ n+1=\pm3 \end{gathered}`

Therefore;

`\begin{gathered} n+1=3 \\ \\ \Rightarrow n=3-1=2 \end{gathered}`

and

`\begin{gathered} n+1=-3 \\ \\ \Rightarrow n=-3-1=-4 \end{gathered}`