1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Square roots and Quad Form

  1. Mar 31, 2009 #1
    1. Sqrt(x)+1=-2Sqrt(x-3)
    1.) Sqrt(x)=-2Sqrt(x-3)-1 ( )^2 gives

    2.) x= (-2sqrt(x-3)-1)^2 and here I think you need to attempt to foil but im not sure how it works.

    3.4sqrt(x-3)+2sqrt(x-3)+2sqrt(x-3)+1=x? Not really sure if this is correct

    2. Relevant equations

    3. First step I subtract 1 from ea side, and take the whole equation to the power of ^2.
    I know for the end of the problem I need to summarize like terms to one side and set it =0 and take the quadratic formula to get 2 answers. 1 will be extraneous.
    Any help is greatly appreciated
  2. jcsd
  3. Mar 31, 2009 #2


    User Avatar
    Science Advisor

    Didn't you forget to multiply the squareroots? (That's the "F" in "FOIL".)
    [itex]4(\sqrt{x-3})^2+ 4\sqrt{x-3}+ 1= x[/itex]
    [itex]4(x-3)+ 4\sqrt{x-3}+ 1= x[/itex]
    [itex]4x- 12+ 4\sqrt{x-3}+ 1= x[/itex]
    [itex]4\sqrt{x-3}= -3x+ 7[/itex]
    Now square again to get rid of that square root.

  4. Apr 6, 2009 #3
    Ok, I think I understood the original problem correctly.
    Here is how I read it:
    [tex]\sqrt{x}[/tex] + 1= -2[tex]\sqrt{x-3}[/tex]
    First thing I would do is square the entire equation. Giving:
    ([tex]\sqrt{x}[/tex] + 1)[tex]^{2}[/tex] = 4(x-3)
    By using the foil method on the left side of the equation and distributing the 4 on the right, you get:
    x + 2[tex]\sqrt{x}[/tex] + 1 = 4x - 12
    Move the x and the 1 to the right side:
    2[tex]\sqrt{x}[/tex] = 3x - 13
    Now you can square again and get rid of the last square root:
    4x = (3x - 13)[tex]^{2}[/tex]
    Foil that:
    4x = 9x[tex]^{2}[/tex] - 78x + 169
    Move the 4x over:
    0 = 9x[tex]^{2}[/tex] - 82x + 169
    Then you're ready to use the quadratic formula!

    Using the method that you originally attempted would work, but foiling with a square root can get confusing. You always have to square the equation twice to get rid of all of the radicals. For me it is easier to foil a square root when there is not a coefficient in front of it, otherwise I end up forgetting to multiply something along the way. Hope this helps!!!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook