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The pattern for completing the square is:

ax² + bx + (b/2)² = c + (b/2)²

But in this quadratic equation, there is no bx, or b = 0:

x² = 16   or   x² - 16 = 0  

Therefore, use extracting the roots for the above example.
If we use completing the square in the example, it will appear like this:

x² + (0/2)² = 16 + (0/2)²
(x-0)² = 16    or  (x)(x) = 16  ⇒What's the point, right?

While you may also use completing the square, it is not the appropriate one.

The only method that is applicable to any quadratic equation is quadratic formula.

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