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If (x − 2)^2 = 100, which of the following could be the value of x + 2

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If (x − 2)^2 = 100, which of the following could be the value of x + 2 [#permalink]

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New post 25 Apr 2017, 11:33
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If (x − 2)^2 = 100, which of the following could be the value of x + 2 ?

A. −10
B. −8
C. −6
D. 10
E. 12

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Re: If (x − 2)^2 = 100, which of the following could be the value of x + 2 [#permalink]

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New post 25 Apr 2017, 11:40
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SajjadAhmad wrote:
If (x − 2)² = 100, which of the following could be the value of x + 2 ?

A. −10
B. −8
C. −6
D. 10
E. 12


If (something)² = 100, then EITHER something = 10 OR something = -10

So, we can conclude that EITHER x − 2 = 10 OR x − 2 = -10

If x − 2 = 10, then x = 12, which means x + 2 = 14
Check answer choices...not there.
Move on.

If x − 2 = -10, then x = -8, which means x + 2 = -6
Check answer choices...BINGO!

Answer:

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Brent
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Re: If (x − 2)^2 = 100, which of the following could be the value of x + 2 [#permalink]

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New post 25 Apr 2017, 17:01
By looking into the options, we can see 12 and -8 are the only possible values for the equation.
Asked us to solve X+2, hence 14 or -6 is our answer.

-6 is only present, hence Option C
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Re: If (x − 2)^2 = 100, which of the following could be the value of x + 2 [#permalink]

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New post 25 Apr 2017, 21:48
Method 1: To take square roots and consider positive/negative values.
Method 2: To solve the quadratic equation with roots 12 and -8
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Re: If (x − 2)^2 = 100, which of the following could be the value of x + 2 [#permalink]

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New post 26 Apr 2017, 00:58
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Re: If (x − 2)^2 = 100, which of the following could be the value of x + 2 [#permalink]

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New post 29 Apr 2017, 09:01
SajjadAhmad wrote:
If (x − 2)^2 = 100, which of the following could be the value of x + 2 ?

A. −10
B. −8
C. −6
D. 10
E. 12


We can simplify the given equation:

√(x − 2)^2 = √100

|x - 2| = 10

We can now solve for when (x - 2) is positive and when it is negative.

When (x - 2) is positive:

x - 2 = 10

x = 12

When (x - 2) is negative:

-(x - 2) = 10

-x + 2 = 10

-x = 8

x = -8

Thus, x + 2 could equal 12 + 2 = 14 or -8 + 2 = -6.

Answer: C
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Re: If (x − 2)^2 = 100, which of the following could be the value of x + 2   [#permalink] 29 Apr 2017, 09:01
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