To solve the equation:

$x^2 - 16 = 0$

we can follow these steps:

1. Rewrite the Equation: Recognize that this is a difference of squares. $x^2 - 16 = (x - 4)(x + 4) = 0$

2. Set Each Factor Equal to Zero: $x - 4 = 0 \quad \text{or} \quad x + 4 = 0$

3. Solve for $x$: $x = 4 \quad \text{or} \quad x = -4$

Solution

The solutions to the equation are: $x = 4 \quad \text{and} \quad x = -4$

Would you like further details or have any questions about this solution?

Here are five related questions:

1. How would the solution change if the equation was $x^2 + 16 = 0$?
2. What is the solution to $x^2 - 25 = 0$?
3. Can you solve $x^2 - 9 = 0$ using the same method?
4. What are the roots of $x^2 - 36 = 0$?
5. How would you solve $x^2 - 1 = 0$ using the difference of squares?

Tip: The difference of squares formula, $a^2 - b^2 = (a - b)(a + b)$, is useful for factoring expressions like this one.