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If (x + 2)^2 = − 4 + 10x , then which of the following could be the va

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If (x + 2)^2 = − 4 + 10x , then which of the following could be the va [#permalink]

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If (x + 2)^2 = − 4 + 10x , then which of the following could be the value of x?

A) 2
B) 1
C) 0
D) −1
E) −2

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Source: Chili Hot GMAT
[Reveal] Spoiler: OA

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Re: If (x + 2)^2 = − 4 + 10x , then which of the following could be the va [#permalink]

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New post 25 Nov 2014, 08:23
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If (x + 2)^2 = − 4 + 10x , then which of the following could be the value of x?

Factor out: x^2 + 4x + 4 = -4 + 10x
Simplify: x^2 - 6x + 8 = 0
Find roots: (x - 4)(x - 2) = 0

Therefore, x = 4 or x = 2 are solutions to the equation. Of the two, only x = 2 is available as answer choice A.
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Re: If (x + 2)^2 = − 4 + 10x , then which of the following could be the va [#permalink]

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New post 25 Nov 2014, 10:13
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Check with plugging values
for x= 2 LHS = RHS
(2 + 2)^2 = − 4 + 10*2
[A]
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Re: If (x + 2)^2 = − 4 + 10x , then which of the following could be the va [#permalink]

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New post 25 Nov 2014, 18:42
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Answer = A) 2

\(x^2 + 4x + 4 = -4 + 10x\)

\(x^2 - 6x + 8 = 0\)

(x - 4)(x - 2) = 0

x = 4 OR x = 2
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Re: If (x + 2)^2 = − 4 + 10x , then which of the following could be the va [#permalink]

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New post 26 Nov 2014, 01:17
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Bunuel wrote:
If (x + 2)^2 = − 4 + 10x , then which of the following could be the value of x?

A) 2
B) 1
C) 0
D) −1
E) −2

Kudos for a correct solution.

Source: Chili Hot GMAT


Solve equation to get x^2-6x+8 = 0 which has solutions x=4 or x=2.
Answer is A.
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Re: If (x + 2)^2 = − 4 + 10x , then which of the following could be the va [#permalink]

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New post 26 Nov 2014, 07:17
Bunuel wrote:
If (x + 2)^2 = − 4 + 10x , then which of the following could be the value of x?

A) 2
B) 1
C) 0
D) −1
E) −2

Kudos for a correct solution.

Source: Chili Hot GMAT


Backsolving

The key to using backsolving is to use the answer choices and see if they work. In this respect, backsolving is like picking numbers except that the numbers we pick are one or more of the actual answer choices. Look for the answer which makes both sides equal. In this particular problem, we may choose to start testing on any single answer choice. Choice A is as good a starting point as any.

Choice A.
(2 + 2)2 = −4 + 10(2)
16 = 16; This is the correct answer since both sides are equal.

Choice B.
(1 + 2)2 = −4 + 10(1); 9 = 6. This is a wrong answer since both sides are not equal.

Choice C.
(0 + 2)2 = −4 + 10(0); 4 = −4. This is a wrong answer since both sides are not equal.

Choice D.
(−1 + 2)2 = −4 + 10(−1); 1 = −14. This is a wrong answer since both sides are not equal.

Choice E.
(−2 + 2)2 = −4 + 10(−2); 0 = −24. This is a wrong answer since both sides are not equal.

Answer: A.
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Re: If (x + 2)^2 = − 4 + 10x , then which of the following could be the va [#permalink]

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New post 26 Nov 2014, 11:34
Simply expand (x+2)^2 and combine all terms on one side of the equation: x^2 + 4x + 4 = -4 + 10x, yielding x^2 -6x + 8=0. The two solutions are 2 and 4.

Choice A
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Re: If (x + 2)^2 = − 4 + 10x , then which of the following could be the va [#permalink]

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New post 29 Oct 2017, 07:20
Bunuel wrote:
If (x + 2)^2 = − 4 + 10x , then which of the following could be the value of x?

A) 2
B) 1
C) 0
D) −1
E) −2


We can simplify the given equation and factor the result:

x^2 + 4x + 4 = -4 + 10x

x^2 - 6x + 8 = 0

(x - 4)(x - 2) = 0

x = 4 or x = 2

Alternate Solution:

Let’s substitute each value in the answer choices for x until we find a value that satisfies the given equation:

A) x = 2

Is (2 + 2)^2 = -4 + 10(2) ?

Is 4^2 = -4 + 20 ?

Is 16 = 16? Yes.

Answer: A
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Re: If (x + 2)^2 = − 4 + 10x , then which of the following could be the va [#permalink]

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New post 29 Oct 2017, 07:37
Bunuel wrote:
If (x + 2)^2 = − 4 + 10x , then which of the following could be the value of x?

A) 2
B) 1
C) 0
D) −1
E) −2

Kudos for a correct solution.

Source: Chili Hot GMAT


\(x^2 + 4 + 4x = -4 + 10x\)

Or, \(x^2 -6x + 8 = 0\)

Or, \(x^2 -4x -2x + 8 = 0\)

Or, \(x(x-4) -2(x-4) = 0\)

Or, \((x-2)(x-4) = 0\)

So, \(x = 2\) or \(x = 4\)

Among the given options, only(A) satisfies, hence, correct answer must be (A)

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Re: If (x + 2)^2 = − 4 + 10x , then which of the following could be the va [#permalink]

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New post 25 Nov 2017, 15:07
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Hi All,

While this question can be solved Algebraically, we're told that one of the numbers IS a solution to the equation - so we can also solve it by TESTing THE ANSWERS. Once we find an answer that 'fits', we can stop working.

Let's start with Answer A: 2... IF X=2, then we have (4)^2 = -4 +2(10).... 16 = 16. Since the equation 'balances', this must the answer.

Final Answer:
[Reveal] Spoiler:
A


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Re: If (x + 2)^2 = − 4 + 10x , then which of the following could be the va   [#permalink] 25 Nov 2017, 15:07
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