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# What is the value of x?

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Director
Joined: 21 Dec 2009
Posts: 520
Concentration: Entrepreneurship, Finance
What is the value of x?  [#permalink]

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29 Nov 2012, 11:02
2
2
00:00

Difficulty:

45% (medium)

Question Stats:

64% (01:44) correct 36% (01:52) wrong based on 180 sessions

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What is the value of x?

(1) 3x^2 + 8x + 16/3 = 0
(2) 15x^2 + 80/3 = -40x

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Math Expert
Joined: 02 Sep 2009
Posts: 51097
What is the value of x?  [#permalink]

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29 Nov 2012, 12:54
What is the value of x?

(1) 3x^2 + 8x + 16/3 = 0 --> multiply by 3: $$9x^2+24x+16=0$$ --> $$(3x+4)^2=0$$ --> $$x=-4/3$$. Sufficient.

(2) 15x^2 + 80/3 = -40x --> multiply by 3/5: $$9x^2+16=-24x$$ --> $$9x^2+24x+16=0$$ --> $$(3x+4)^2=0$$ --> $$x=-4/3$$. Sufficient.

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Director
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Re: What is the value of x?  [#permalink]

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29 Nov 2012, 14:49
1
0k, that's a perfect square.
Otherwise, I reduced to the standard quadratic form: ax^2 + bx + c and factorize.
9x^2 + 24x + 16 = 0
9x^2 + 12x + 12x + 16 = 0
3x(3x+4) + 4(3x+4)=0
(3x + 4)^2 = 0

Or,
x^2 + (8/3)x + (4/3)^2 = 0 [(8/3)^2 = 4*(1)(16/9)]
(x + 4/3)^2 = 0....x= -4/3
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Joined: 17 Jul 2014
Posts: 2621
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: What is the value of x?  [#permalink]

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05 Apr 2016, 17:21
gmatbull wrote:
What is the value of x?

(1) 3x^2 + 8x + 16/3 = 0
(2) 15x^2 + 80/3 = -40x

1 can be rewritten as (3x+4)^2 so we can find X.
2. can be rewritten as:
45x^2 + 80 +120x = 0
divide by 5:
9x^2 + 16+24x=0
basically the same equation
we can factor out (3x+4)^2 = 0

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Concentration: General Management, Finance
Schools: WHU MBA"20 (WL)
GMAT 1: 740 Q49 V41
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WE: Engineering (Other)
What is the value of x?  [#permalink]

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27 Jul 2017, 07:35
for those like me who did not find square immediately:

for equation in form:
$$ax^2+bx+c=0$$

has the unique solution if:
$$b^2-4ac=0$$

Be careful with the $$+$$ and $$-$$ signs though. I often have confused myself with signs.
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Re: What is the value of x?  [#permalink]

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07 Aug 2018, 10:29
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: What is the value of x? &nbs [#permalink] 07 Aug 2018, 10:29
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