Solve the given equation by the zero-factor property.
\[
x^{2}-16=0
\]

Answer

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Answer

Final Answer: The solutions to the equation are \(\boxed{-4}\) and \(\boxed{4}\).

Steps

Step 1 ：Given the equation \(x^{2}-16=0\).

Step 2 ：We can rewrite the equation as a product of two factors by factoring the difference of squares.

Step 3 ：Factoring the equation gives us \((x-4)(x+4)=0\).

Step 4 ：According to the zero-factor property, if the product of two factors is zero, then at least one of the factors must be zero.

Step 5 ：So, we set each factor equal to zero and solve for x: \(x-4=0\) and \(x+4=0\).

Step 6 ：Solving these equations gives us the solutions \(x=4\) and \(x=-4\).

Step 7 ：Final Answer: The solutions to the equation are \(\boxed{-4}\) and \(\boxed{4}\).