To solve the equation 18x² = 64, we need to isolate the variable x.

First, divide both sides of the equation by 18:

(18x²)/18 = 64/18

Simplifying, we get:

x² = 64/18

Next, take the square root of both sides of the equation:

√(x²) = √(64/18)

Simplifying further:

x = ±√(64/18)

Now, let's simplify the square root of 64/18:

x = ±√(64)/√(18)

x = ±8/√(18)

To rationalize the denominator, multiply both the numerator and denominator by √(18):

x = (±8/√(18)) * (√(18)/√(18))

x = ±(8√(18))/18

Simplifying the expression:

x = ±(4√(2))/9

Therefore, the solutions to the equation 18x² = 64 are x = (4√(2))/9 and x = -(4√(2))/9.