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What is the value of x? (1) 3x^2 + 8x + 16/3 = 0 (2) 15x^2 + 80/3 = -4

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Joined: 21 Dec 2009
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What is the value of x? (1) 3x^2 + 8x + 16/3 = 0 (2) 15x^2 + 80/3 = -4  [#permalink]

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29 Nov 2012, 12:02
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Question Stats:

64% (01:51) correct 36% (01:56) wrong based on 212 sessions

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What is the value of x?

(1) $$3x^2 + 8x + \frac{16}{3} = 0$$

(2) $$15x^2 + \frac{80}{3} = -40x$$

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Re: What is the value of x? (1) 3x^2 + 8x + 16/3 = 0 (2) 15x^2 + 80/3 = -4  [#permalink]

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29 Nov 2012, 13:54
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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Re: What is the value of x? (1) 3x^2 + 8x + 16/3 = 0 (2) 15x^2 + 80/3 = -4  [#permalink]

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29 Nov 2012, 15:49
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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Re: What is the value of x? (1) 3x^2 + 8x + 16/3 = 0 (2) 15x^2 + 80/3 = -4  [#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

D
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Re: What is the value of x? (1) 3x^2 + 8x + 16/3 = 0 (2) 15x^2 + 80/3 = -4  [#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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Re: What is the value of x? (1) 3x^2 + 8x + 16/3 = 0 (2) 15x^2 + 80/3 = -4  [#permalink]

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03 Dec 2017, 00:23
1
(1) 3x^2 + 8x + 16/3 = 0 can be rewritten as
9x^2 + 24x + 16 = 0.. OR (3x+4)^2 = 0
This gives us x=-4/3. Sufficient.

(2) 15x^2 + 80/3 = -40x can be rewritten as
15x^2 + 40x + 80/3 = 0 .. Dividing this by 5, we get
5x^2 + 8x + 16/3 = 0. This is same as the equation in statement 1, and will give us same value of x. Sufficient.

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Re: What is the value of x? (1) 3x^2 + 8x + 16/3 = 0 (2) 15x^2 + 80/3 = -4  [#permalink]

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24 Dec 2018, 05:43
1
gmatbull wrote:
What is the value of x?

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

Dear Moderator,
This same question has been Duplicated in the link below, you may wish to merge the same. Thank you.

https://gmatclub.com/forum/what-is-the- ... l#p1972082
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Re: What is the value of x? (1) 3x^2 + 8x + 16/3 = 0 (2) 15x^2 + 80/3 = -4  [#permalink]

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24 Dec 2018, 05:47
stne wrote:
gmatbull wrote:
What is the value of x?

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

Dear Moderator,
This same question has been Duplicated in the link below, you may wish to merge the same. Thank you.

https://gmatclub.com/forum/what-is-the- ... l#p1972082

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Topics Merged. Thank you.
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Re: What is the value of x? (1) 3x^2 + 8x + 16/3 = 0 (2) 15x^2 + 80/3 = -4   [#permalink] 24 Dec 2018, 05:47
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