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Solving For X on both sides

  1. Mar 24, 2009 #1
    1. The problem statement, all variables and given/known data
    A basic example is [tex]\sqrt{x-1}[/tex]=x-7


    2. Relevant equations



    3. The attempt at a solution
    I end up with an x[tex]^{2}[/tex] and a normal x I dont know to to solve it.
     
  2. jcsd
  3. Mar 24, 2009 #2

    Integral

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    Please show us your work. You say you have and x2. ok, you should have an x2 term, now show us exactly what you have and how you got it.
     
  4. Mar 24, 2009 #3

    HallsofIvy

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    So that's a quadratic equation, isn't it? You can solve quadratic equations by factoring, completing the square, or using the quadratic formula.
     
  5. Mar 24, 2009 #4
    I thought this was a radical equation? Not a quadric one. If this is a quadric one I dont have to worry abought that yet then.
    How do you solve somthing with a root on both side then? Like [tex]\sqrt{3x+2}[/tex] + [tex]\sqrt{2x}[/tex]= 35, I keep getting an answer thats too high.
     
    Last edited: Mar 24, 2009
  6. Mar 24, 2009 #5

    Office_Shredder

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    Turn it into

    [tex] \sqrt{3x+2} = 35 - \sqrt{2x}[/tex]

    square both sides

    [tex]3x+2 = 35^2 + 2x - 70 \sqrt{2x}[/tex]

    and now you only have one square root
     
  7. Mar 24, 2009 #6

    symbolipoint

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    Stratosphere, your first example, [tex]\sqrt{x-1}[/tex] = x - 7, should give you no complications when you square both sides. It WILL give you a quadratic equation. Either you can (after suitable algebraic steps) factor and solve, or you can complete the square/use solution to quadratic equation to solve.
     
  8. Mar 24, 2009 #7
    were does the -70 come from?
     
  9. Mar 24, 2009 #8
    [tex] (35-\sqrt{2x})^2 [/tex]

    Expand it out.
     
  10. Mar 24, 2009 #9
    Don't forget, when you square the radical, you can end up finding solutions for x that do not work. You have to go through and check these solutions with your original equation to make sure that each value works.
     
  11. Mar 25, 2009 #10
    Oh and how do you know what is a,b and c when using the quadratic formula?
     
  12. Mar 26, 2009 #11
    The general form of a quadratic equation is [tex]ax^{2} + bx + c = 0[/tex]. Hopefully that answers your question. ;)


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