To solve the equation (3-x)² = 1/16, we can take the square root of both sides:

√((3-x)²) = √(1/16)

Simplifying the square root of the left side:

3-x = ±√(1/16)

Now, let's simplify the square root of 1/16:

√(1/16) = 1/4

Substituting this back into the equation:

3-x = ±(1/4)

To solve for x, we can isolate it by subtracting 3 from both sides:

-x = ±(1/4) - 3

Now, let's simplify the right side:

-x = ±(1/4) - 12/4

-x = ±(1 - 12)/4

-x = ±(-11)/4

To get rid of the negative sign, we can multiply both sides by -1:

x = ±(11/4)

Therefore, the solutions to the equation (3-x)² = 1/16 are x = 11/4 and x = -11/4.