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

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02 Nov 2018, 02:26
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Difficulty:

5% (low)

Question Stats:

85% (01:23) correct 15% (01:21) wrong based on 55 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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Re: If (x^2 + 6x + 9) + 6(x+3) + 9 = 0, then x=  [#permalink]

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02 Nov 2018, 02:49
2
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

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Re: If (x^2 + 6x + 9) + 6(x+3) + 9 = 0, then x=  [#permalink]

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21 Feb 2019, 14:24
Top Contributor
pushpitkc wrote:
If $$(x^2 + 6x + 9) + 6(x+3) + 9 = 0$$, then x=

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

Alternatively, we can simplify and solve the given equation

GIVEN: (x² + 6x + 9) + 6(x+3) + 9 = 0
Expand left side to get: x² + 6x + 9 + 6x + 18 + 9 = 0
Simplify left side to get: x² + 12x + 36 = 0
Factor left side to get: (x + 6)(x + 6) = 0
So, it must be the case that (x + 6) = 0
If x + 6 = 0, then x = -6

Cheers,
Brent
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Re: If (x^2 + 6x + 9) + 6(x+3) + 9 = 0, then x=  [#permalink]

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21 Feb 2019, 15:39
pushpitkc wrote:
If $$(x^2 + 6x + 9) + 6(x+3) + 9 = 0$$, then x=

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

Given ,

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

$$(x+3)^2 + 6(x + 3) = -9$$

(x+3) {(x + 3 + 6)} = -9

(x + 3) ( x + 9) = -9.

Option A works.

x = -6.
Re: If (x^2 + 6x + 9) + 6(x+3) + 9 = 0, then x=   [#permalink] 21 Feb 2019, 15:39
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