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The solutions are 8 and -8

Explanation:
Before we begin, remember the rule of the difference between squares which is as follows:
x² - a² = (x+a)(x-a)

Now, for the given, we have:
x² - 64 = 0
This is equivalent to:
x² - (8)² = 0

Applying the rule of the difference between squares mentioned above, we would factorize the equation as follows:
(x-8)(x+8) = 0
This means that:
either x-8 = 0 > x = 8
or x+8 = 0 > x = -8

Based on the above, the solutions would be: 8 and -8

Hope this helps :)