To solve for x in the equation 2cos(2x) = -√2, we can first isolate the cosine term by dividing both sides by 2:

cos(2x) = -√2 / 2

Next, we know that the cosine function has a range of -1 to 1, so for this equation to be true, -√2 / 2 must be in that range. However, since -√2 / 2 is not within that range, there are no solutions for x that satisfy the equation 2cos(2x) = -√2.