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# What is the value of x?

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

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29 Nov 2012, 12:02
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What is the value of x?

(1) 3x^2 + 8x + 16/3 = 0
(2) 15x^2 + 80/3 = -40x
[Reveal] Spoiler: OA

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What is the value of x? [#permalink]

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29 Nov 2012, 13:54
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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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Re: What is the value of x? [#permalink]

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29 Nov 2012, 15:49
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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Re: What is the value of x? [#permalink]

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28 Aug 2014, 05:22
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Re: What is the value of x? [#permalink]

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24 Feb 2016, 20:27
Hello from the GMAT Club BumpBot!

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

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05 Apr 2016, 18:21
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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What is the value of x? [#permalink]

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27 Jul 2017, 08:35
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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What is the value of x?   [#permalink] 27 Jul 2017, 08:35
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