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# If x^2 + 0.25x - 0.5 = 0, then x(4x + 1) =

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Math Expert
Joined: 02 Sep 2009
Posts: 49968
If x^2 + 0.25x - 0.5 = 0, then x(4x + 1) =  [#permalink]

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17 Sep 2017, 03:45
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Difficulty:

15% (low)

Question Stats:

85% (01:15) correct 15% (02:38) wrong based on 58 sessions

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If x^2 + 0.25x - 0.5 = 0, then x(4x + 1) =

A. 0.5
B. 2
C. 3.5
D. 4
E. 0

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Joined: 19 Sep 2016
Posts: 35
Re: If x^2 + 0.25x - 0.5 = 0, then x(4x + 1) =  [#permalink]

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17 Sep 2017, 04:09
X(x+.25)=.5, either x=.5 or x=.25. Now substituting these values in the required equation, x(4x+1)= either 1.5 or .5. So answer is A.

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Joined: 19 Sep 2016
Posts: 35
Re: If x^2 + 0.25x - 0.5 = 0, then x(4x + 1) =  [#permalink]

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17 Sep 2017, 04:47
Sorry. Correcting the answer is B i.e. 2

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Re: If x^2 + 0.25x - 0.5 = 0, then x(4x + 1) =  [#permalink]

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17 Sep 2017, 07:55
Bunuel wrote:
If x^2 + 0.25x - 0.5 = 0, then x(4x + 1) =

A. 0.5
B. 2
C. 3.5
D. 4
E. 0

x^2+1/4x= 1/2;

4x^2+x= 2 ==> x(4x+1)= 2

Ans:B
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Joined: 22 May 2016
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If x^2 + 0.25x - 0.5 = 0, then x(4x + 1) =  [#permalink]

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17 Sep 2017, 15:01
Bunuel wrote:
If x^2 + 0.25x - 0.5 = 0, then x(4x + 1) =

A. 0.5
B. 2
C. 3.5
D. 4
E. 0

$$x^2 + 0.25x - 0.5 = 0$$

Multiply by 4: prompt's second expression is a factored version of $$4x^2 + x$$. That expression = $$(4)(x^2 + 0.25x)$$ -- i.e., (4) * the first two terms of the quadratic equation

$$(4)x^2 + (4)0.25x - (4)0.5 = 0$$
$$4x^2 + x - 2 = 0$$
$$4x^2 + x = 2$$
$$x(4x + 1) = 2$$

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Re: If x^2 + 0.25x - 0.5 = 0, then x(4x + 1) =  [#permalink]

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18 Sep 2017, 11:53
x^2 + .25x -.5=0
can be written as x^2 + x/4 -5/10=0
now, x( x+1/4)=5/10
multiple by 4 on both sides
you get 4x^2+x=2 i.e x(4x+1)=2
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Re: If x^2 + 0.25x - 0.5 = 0, then x(4x + 1) =  [#permalink]

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18 Sep 2017, 12:03
x^2 + (x/4) =1/2
x(4x +1) = 2 so Ans is B.
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Re: If x^2 + 0.25x - 0.5 = 0, then x(4x + 1) =  [#permalink]

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22 Sep 2017, 11:45
Bunuel wrote:
If x^2 + 0.25x - 0.5 = 0, then x(4x + 1) =

A. 0.5
B. 2
C. 3.5
D. 4
E. 0

We need to determine the value of x(4x + 1) = 4x^2 + x.

Multiplying the equation x^2 + 0.25x - 0.5 = 0 by 4, we have:

4x^2 + x - 2 = 0

4x^2 + x = 2

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Re: If x^2 + 0.25x - 0.5 = 0, then x(4x + 1) = &nbs [#permalink] 22 Sep 2017, 11:45
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