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Math Help - Rewriting Equations

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by CzWJF41 View Post
    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?
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  3. #3
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    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.
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  4. #4
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    Rewriting Equations

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