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

Question

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

BrentGMATPrepNow · Answer

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:  C

Cheers,
Brent

umadurga · Answer

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

warriorguy · Answer

Method 1: To take square roots and consider positive/negative values.
Method 2: To solve the quadratic equation with roots 12 and -8

Bunuel · Answer

JeffTargetTestPrep · Answer

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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