Solve for x: x² - 16 = 0.

To solve the equation ( x^2 - 16 = 0 ), the first step is to recognize that this is a difference of squares. The expression can be factored using the formula ( a^2 - b^2 = (a - b)(a + b) ). Here, ( a ) is ( x ) and ( b ) is ( 4 ), since ( 16 ) is ( 4^2 ).

Factoring the equation yields:

[

(x - 4)(x + 4) = 0

]

This product will equal zero if either factor is zero. Therefore, we set each factor equal to zero:

1. ( x - 4 = 0 ) leads to ( x = 4 )

2. ( x + 4 = 0 ) leads to ( x = -4 )

Thus, the solutions to the equation ( x^2 - 16 = 0 ) are ( x = 4 ) and ( x = -4 ). This confirms that the correct answer reflects the values of ( x ) derived from solving the equation, which are both ( 4 ) and ( -4 \