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Simplifying Equation With Square Root

  1. Jan 26, 2008 #1
    1. The problem statement, all variables and given/known data
    An equation in a book lists this equation:
    (c - 18)[tex]^{2}[/tex] = (-3[tex]\sqrt{c})[/tex][tex]^{2}[/tex]

    And it simplifies it as:
    c[tex]^{2}[/tex] -45c + 324 = 0

    2. The attempt at a solution
    When I do out the equation, I get:
    c[tex]^{2}[/tex] + 324 = 9 + c

    i squared c, then -18 for the left side of the equation, then for the right side, I squared -3 to get 9, then [tex]\sqrt{c}[/tex], which is c.
    Last edited: Jan 26, 2008
  2. jcsd
  3. Jan 26, 2008 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    Hi kwikness and welcome to PF,

    Firstly, note that;

    [tex]\left(a+b\right)^2 \neq a^2+b^2[/tex]


    [tex]\left(a+b\right)^2 = \left(a+b\right)\cdot\left(a+b\right) = a^2 +2ab + b^2[/tex]


    [tex](-3)^2 \neq 324[/tex]

    And thirdly;

    [tex](a\cdot b)^2 \neq a^2+b^2[/tex]


    [tex](a\cdot b)^2 = a^2\cdot b^2[/tex]
    Last edited: Jan 26, 2008
  4. Jan 26, 2008 #3
    Sorry, I meant 9 =)

    I made my mistake when I forgot to "FOIL" the left-hand side of the equation. When I do so, I get:

    C[tex]^{2}[/tex] -45c + 324 = 0

    Thank you very much for clearing that up for me. I'm in a bit of a situation. I'm a good student in my 4th semester of college. In high school, I was able to slide by my math classes. I half-assed Algebra I, did okay in Geometry, and took no other math courses. Now I find myself in Calculus I, 5 years after my last math class. The first thing my professor said was, "You're not going to pass this course unless you've had Trigonometry and Pre-Calculus.", which I haven't. I'm now trying to backtrack and learn these courses myself with the aid of video tutorials and practicing problems on my own time. I excel in every subject at school but math. It's such a weakness for me and I'm now just starting to do something about it.

    Any pointers are appreciated, thanks again for your help.
  5. Jan 27, 2008 #4


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    Staff: Mentor

    One needs to know the solution to the quadratic equation.

    Alternatively, one recognizes (c+a)(c+b) = c2 + (a+b)c + ab = c2 - 45c + 324, so what does one do with corresponding coefficients?
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