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math problem

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math problem [#permalink] New post 13 Sep 2008, 01:50
(x^2 + 6x +9) + 6(x+3) + 9 = 0, then x= ??

The answer is -6. Can you please advise how you get to this answer?
Many thanks,
Andreas
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Re: math problem [#permalink] New post 13 Sep 2008, 07:01
factoring gives you (x+6)(x+6)=0 [check: x^2+6x+6x+36 = x^2+12x+36].
so (x+6)(x+6), mean the ansewr is -6 or -6....i.e. -6.
substitute in the original form to get check (you will get 0=0)
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Re: math problem [#permalink] New post 13 Sep 2008, 14:02
thats great ! Thank you !
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Re: math problem [#permalink] New post 13 Sep 2008, 18:35
Yeah... just multiply out 6(x+3) and sum:

x^2 + 6x + 9 + 6x + 18 + 9 = 0

x^2 + 12x + 36 = 0

( x+6)(x+6) = 0

-6 is answer
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Re: math problem [#permalink] New post 14 Sep 2008, 09:29
Here's a slightly different approach.

You recognize that original equation has the form a^2+2ab+b^2=(a+b)^2
with a=(x+3) and b = 3.

Therefore the original equation can be written as

(x+3+3)^2=0 ===> x = - 6
Re: math problem   [#permalink] 14 Sep 2008, 09:29
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