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Thread: Re-arranging formula question

  1. #1
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    Re-arranging formula question

    Hi All,

    I'm having a slight problem with a re-arranging formula question (not a marked one, the answers are on the sheet, I just don't know how to get to the specified answer) it should be easy and I'm pretty embarrassed that I can't do it.

    The question is make 'x' the subject of:
    $\displaystyle r^2 = (x - a)^2 + y^2$

    According to the sheet the correct answer is
    $\displaystyle x = sqrt(r^2 - y^2) + a$

    I've tried it various ways though and usually end up with
    $\displaystyle x = r - y + a$

    If anyone could break down how you get the correct answer that would be great. Thanks in advance.
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  2. #2
    Super Member 11rdc11's Avatar
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    $\displaystyle r^2 = (x-a)^2 + y^2$

    $\displaystyle r^2 - y^2 = (x-a)^2$

    Take square root of both sides

    $\displaystyle \sqrt{r^2-y^2} = x-a$

    $\displaystyle \sqrt{r^2-y^2} + a =x$
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  3. #3
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    Doh, that was easy, now I feel even more stupid.

    Thanks.

    I'm having problem with another easy one if you could help

    Make 'x' the formula of:

    $\displaystyle y = c/(x+a)$

    with the answer being:
    $\displaystyle x = (c/y) - a$

    I did...

    $\displaystyle y = c/(x+a)$
    $\displaystyle y(x + a) = c$
    $\displaystyle yx + ya = c$
    $\displaystyle yx = c - ya$
    $\displaystyle x = (c - ya)/y$

    but apparently I seem to have wrong somewhere (or just not simplified it enough?). Thanks again.
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  4. #4
    Super Member 11rdc11's Avatar
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    $\displaystyle y = \frac{c}{x+a}$

    $\displaystyle y(x+a) = c$

    $\displaystyle x+a = \frac{c}{y}$

    $\displaystyle x = \frac{c}{y} -a$
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  5. #5
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    Thank you, again! That's been a great help.
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