To solve the equation sin(3x + π/2) = -√2/2, we can use the inverse sine function.

First, let's find the reference angle for -√2/2, which is π/4. This means that sin(π/4) = -√2/2.

Now, we can rewrite the equation as 3x + π/2 = π/4.

Subtracting π/2 from both sides, we get 3x = π/4 - π/2.

Simplifying the right side, we have 3x = -π/4.

Dividing both sides by 3, we get x = -π/12.

So, the solution to the equation sin(3x + π/2) = -√2/2 is x = -π/12.