Can someone please correct my algebra here?

• Apr 12th 2014, 03:01 PM
blaisem
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!
• Apr 13th 2014, 03:12 PM
HallsofIvy
Re: Can someone please correct my algebra here?
Quote:

Originally Posted by blaisem
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.

Quote:

(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!
• Apr 14th 2014, 04:54 AM
blaisem
Re: Can someone please correct my algebra here?
Got it, thanks ;)