1. ## Rewriting Equations

Hello everyone,

I was given a problem in my math textbook, which is for my Algebra 2 class. It is in the section for "Rewriting Equations" and it says:

"Solve the formula: t = a + n (n - 1 )d for n"

I was looking through the examples, and maybe it is just not me understanding but I just can't understand what to do here. Thanks in advance for anyone who can help me out.

2. Originally Posted by CzWJF41
Hello everyone,

I was given a problem in my math textbook, which is for my Algebra 2 class. It is in the section for "Rewriting Equations" and it says:

"Solve the formula: t = a + n (n - 1 )d for n"

I was looking through the examples, and maybe it is just not me understanding but I just can't understand what to do here. Thanks in advance for anyone who can help me out.
Lets move a over to the other side first to get
$t-a=n(n-1)d$

Now let's divide by d to get
$\frac{t-a}{d}=n(n-1)$

And expand the right hand side to get
$\frac{t-a}{d}=n^2-n$

And now we'll "complete the square" by adding $\frac{1}{4}$ to both sides to get
$\frac{t-a}{d}+\frac{1}{4}=n^2-n+\frac{1}{4}$

Now we'll need a common denominator to add the fractions and we'll also factor the right hand side to get
$\frac{4(t-a)}{4d}+\frac{d}{4d}=(n-\frac{1}{2})^2$

And can you take it from here?

3. Thanks a lot. I should be able to do this from here... this definitely helped from staring at the page for minutes. Thanks again, I really appreciate this.

4. ## Rewriting Equations

whoops double post, sorry... thought I was doing something else... stupid mistake, any way I can delete this?