To solve this equation for x, we can first rewrite it as:

2sin(\pi/6+x) = \sqrt{2}

Next, we divide both sides by 2 to isolate the sine term:

sin(\pi/6+x) = \sqrt{2}/2

Now, we know that sin(\pi/6) = 1/2. So, we can rewrite the equation as:

sin(\pi/6)cos(x) + cos(\pi/6)sin(x) = sqrt(2)/2

Now, we can substitute sin(\pi/6) = 1/2 and cos(\pi/6) = sqrt(3)/2 into the equation:

(1/2)cos(x) + (sqrt(3)/2)sin(x) = sqrt(2)/2

Now we can use the trigonometric identity sin^2(x) + cos^2(x) = 1 to rewrite the equation as:

cos(x) = sqrt(2)/2

Solving for x, we get:

x = acos(sqrt(2)/2)

Since cos(45 degrees) = sqrt(2)/2, a possible solution for x is x = 45 degrees or x = pi/4 radians.