If \(2^{2x+5}-65\cdot 2^{x+1}=-8,\) then which of the following statement is definitely correct?

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If \(2^{2x+5}-65\cdot 2^{x+1}=-8,\) then which of the following statement is definitely correct?

A. \(x\) can only be a positive integer
B. \(x\) can only be a negative integer
C. \(x\) can be either a positive integer or a negative integer
D. No value of \(x\) exists which satisfies the equation
E. \(x\) is not an integer

Answer: C

Source: e-GMAT
Source: — Problem Solving |