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# If (x^2 + 6x + 9) + 6(x+3) + 9 = 0, then x=

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Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3334
Location: India
GPA: 3.12
If (x^2 + 6x + 9) + 6(x+3) + 9 = 0, then x=  [#permalink]

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02 Nov 2018, 01:26
00:00

Difficulty:

15% (low)

Question Stats:

81% (01:25) correct 19% (01:04) wrong based on 26 sessions

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If $$(x^2 + 6x + 9) + 6(x+3) + 9 = 0$$, then x=

(A) -6
(B) -3
(C) 0
(D) 3
(E) 6

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Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 652
Re: If (x^2 + 6x + 9) + 6(x+3) + 9 = 0, then x=  [#permalink]

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02 Nov 2018, 01:49
1
On careful observation we notice that the expression inside the first paranthesis is square of $$x+3$$
$$(x^2 + 6x + 9) + 6(x+3) + 9 = 0$$

Hence we can denote x+3 by a new variable t.

Expression becomes...
$$t^2+6t+9=0$$
$$(t+3)^2=0$$
$$t=-3$$
Substitute back to get original variable
$$x+3=-3$$
$$x = -6$$

Hence Option (A) is our choice.

Best,

pushpitkc wrote:
If $$(x^2 + 6x + 9) + 6(x+3) + 9 = 0$$, then x=

(A) -6
(B) -3
(C) 0
(D) 3
(E) 6

_________________

Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)

Re: If (x^2 + 6x + 9) + 6(x+3) + 9 = 0, then x= &nbs [#permalink] 02 Nov 2018, 01:49
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