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Math Help - Can someone please correct my algebra here?

  1. #1
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    Can someone please correct my algebra here?

    Nevermind, I found the error while editing this post! Good thing I shared this, sorry for the forum clutter! I don't know how to delete the thread.

    Hi, I have a problem that looks like this:

    (1)
    L = 7.5B + 15D (+-) 0.5\sqrt{225B^2 + 100D^2 - 180(D*B)}

    L = 28490
    D = 2183

    Solve for B.

    The solution gives B = 622

    Values may have been rounded at various steps during their derivation, so some error of around 10-30 may occur.

    This formula is derived from the notes and used to solve a problem from the professor. The (+-) indicates that in the notes, a minus(-) sign is used, while in the professor's solution set, he uses a plus(+). When I plug in the correct numbers using the solution, it seems a minus (-) is correct; however, in solving for B, I have to square both sides, so I don't see how the plus/minus (+-) should matter. This confuses me that when I work the problem backwards using B to solve for L, the minus is important, but when I solve for B, I cannot for the world of me see its relevance.

    Here's my work:

    (1)
    L = 7.5B + 15D + 0.5\sqrt{225B^2 + 100D^2 - 180(D*B)}

    (2)
     L - 7.5B - 15D =  0.5\sqrt{225B^2 + 100D^2 - 180(D*B)}

    (3)
     2L - 15B - 30D =  \sqrt{225B^2 + 100D^2 - 180(D*B)}

    (4)
     (2L - 15B - 30D)^2 =  225B^2 + 100D^2 - 180(D*B)

    (5)
     4L^2 + 225B^2 +900D^2 - 60(L*B) - 120(L*D) + 450(D*B) = 225B^2 + 100D^2 - 180(D*B)

    (6)
     4L^2 + 800D^2 - 120(L*D) = 60(L*B) - 630(D*B)

    (7)
     \frac{4[L^2 + 200D^2 - 30(L*D)]}{60L - 630D} = B

    L = 28490
    D = 2183

    I get about B = -1209 units. B should equal 622.

    Arbitrarily removing the negative and dividing by two, it's close enough that it might be the correct value of B (622), but of course that may also be coincidence.

    Anyone see what I am doing wrong? It seems that when I work the problem backwards using the solution, I get the right answers. So it must be my simplification somewhere...

    Thanks so much for any pointers! I appreciate it.

    Edit: Got 623 as answer. My D * B expansion I forgot to multiply in both directions while expanding the polynomial. Should have been 900 (D*B), not 450 (D*B)

    Thanks anyways to anyone who read!
    Last edited by blaisem; April 12th 2014 at 03:16 PM.
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  2. #2
    MHF Contributor

    Joined
    Apr 2005
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    1789

    Re: Can someone please correct my algebra here?

    Quote Originally Posted by blaisem View Post
    Nevermind, I found the error while editing this post! Good thing I shared this, sorry for the forum clutter! I don't know how to delete the thread.

    Hi, I have a problem that looks like this:

    (1)
    L = 7.5B + 15D (+-) 0.5\sqrt{225B^2 + 100D^2 - 180(D*B)}

    L = 28490
    D = 2183

    Solve for B.

    The solution gives B = 622

    Values may have been rounded at various steps during their derivation, so some error of around 10-30 may occur.

    This formula is derived from the notes and used to solve a problem from the professor. The (+-) indicates that in the notes, a minus(-) sign is used, while in the professor's solution set, he uses a plus(+). When I plug in the correct numbers using the solution, it seems a minus (-) is correct; however, in solving for B, I have to square both sides, so I don't see how the plus/minus (+-) should matter. This confuses me that when I work the problem backwards using B to solve for L, the minus is important, but when I solve for B, I cannot for the world of me see its relevance.

    Here's my work:

    (1)
    L = 7.5B + 15D + 0.5\sqrt{225B^2 + 100D^2 - 180(D*B)}

    (2)
     L - 7.5B - 15D =  0.5\sqrt{225B^2 + 100D^2 - 180(D*B)}

    (3)
     2L - 15B - 30D =  \sqrt{225B^2 + 100D^2 - 180(D*B)}

    (4)
     (2L - 15B - 30D)^2 =  225B^2 + 100D^2 - 180(D*B)

    (5)
     4L^2 + 225B^2 +900D^2 - 60(L*B) - 120(L*D) + 450(D*B) = 225B^2 + 100D^2 - 180(D*B)
    You appear to have forgotten the "2" in the "D*B" term on the left- 2(15)(30)= 2(450)= 900.

    (6)
     4L^2 + 800D^2 - 120(L*D) = 60(L*B) - 630(D*B)

    (7)
     \frac{4[L^2 + 200D^2 - 30(L*D)]}{60L - 630D} = B

    L = 28490
    D = 2183

    I get about B = -1209 units. B should equal 622.

    Arbitrarily removing the negative and dividing by two, it's close enough that it might be the correct value of B (622), but of course that may also be coincidence.

    Anyone see what I am doing wrong? It seems that when I work the problem backwards using the solution, I get the right answers. So it must be my simplification somewhere...

    Thanks so much for any pointers! I appreciate it.

    Edit: Got 623 as answer. My D * B expansion I forgot to multiply in both directions while expanding the polynomial. Should have been 900 (D*B), not 450 (D*B)

    Thanks anyways to anyone who read!
    Thanks from blaisem
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  3. #3
    Newbie
    Joined
    Oct 2012
    From
    Germany
    Posts
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    Re: Can someone please correct my algebra here?

    Got it, thanks
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