SOLUTION: Hi. May I have some help with the following equation? Find all real solutions of the following equation. (If there are extra answer boxes, enter NONE.) (x/(x+7))^2 = (4 x)/(x

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Question 121277: Hi. May I have some help with the following equation?
Find all real solutions of the following equation. (If there are extra answer boxes, enter NONE.)
(x/(x+7))^2 = (4 x)/(x+7) - 4
Found 2 solutions by stanbon, checkley71:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
(x/(x+7))^2 = 4( x)(x+7) - 4
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Let w = x/(x+7)
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Rewrite to get:
w^2 - 4w - 4 = 0
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Comment: I suspect you have a sign wrong in your posting.
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Cheers,
Stan H.

Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website!
(X/(X+7))^2=(4X)/(X+7)-4
X^2/(X^2+14X+49)=4X/(X+7)-4
X^2/(X^2+14X+49)=(4X-4(X+7))/(X+7)
X^2/(X^2+14X+49)=(4X-4X-28)/(X+7)
X^2/(X^2+14X+49)=-28/(X+7) NOW CROSS MULTIPLY
X^2(X+7)=-28(X^2+14X+49)
X^2(X+7)=-28(X+7)(X+7) DIVIDE BOTH SIDES BY (X+7)
X^2=-28X-196
X^2+28X+196=0
(X+14)^2=0
X+14=0
X=-14 ANSWER.
PROOF
[-14/(-14+7)]^2=4*-14/(-14+7)-4
(-14/-7)^2=-56/-7-4
2^2=8-4
4=4