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Simple equation?

  1. Sep 21, 2004 #1
    3.4 10

    [tex]
    2x+3\sqrt{3x-5}=5
    [/tex]

    [tex]
    3\sqrt{3x-5}=5-2x \ \ \ \ \ \ \mid ()^2
    [/tex]

    [tex]
    \\9(3x-5)=25+2*5*(-2x)+(2x)^2
    [/tex]

    [tex]
    \\27x-45=25-20x+4x^2
    [/tex]

    [tex]
    \\27x+20x-4x^2=25+45
    [/tex]

    [tex]
    \\47x-4x^2=70
    [/tex]

    [tex]
    \\-4x^2+47x-70=0
    [/tex]

    hmhph

    [tex]
    x= \frac { -47^+_- \sqrt {47^2-4*(-4)*-(70)}}{2*-4}
    [/tex]


    [tex]
    x= \frac { -47^+_-33}{-8}
    [/tex]

    [tex]
    x= \ 10 \ or \ x= \ \frac {7}{4}
    [/tex]
     
    Last edited: Sep 21, 2004
  2. jcsd
  3. Sep 21, 2004 #2
    It seems right.

    What exactly is your question here?
     
  4. Sep 21, 2004 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I hope you realize that writing
    [tex]\\x \left( x - \frac {47}{4} \right) = \frac{70}{4}[/tex]
    doesn't help you at all: if ab=0 then either a=0 or b= 0 but that only works for "= 0".

    You could have written [itex]4x^2- 47x-70=0[/itex] and perhaps have reconized that this can be factored: (x-10)(4x-7) but I will confess that I got that by looking at your solution!
     
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