To find $x$ in the equation:

$x^2 - 1 = 0$

we can solve it step by step:

1. Add 1 to both sides of the equation: $x^2 - 1 + 1 = 0 + 1$ This simplifies to: $x^2 = 1$

2. Take the square root of both sides: $\sqrt{x^2} = \pm \sqrt{1}$ So, $x = \pm 1$.

Thus, the solutions are $x = 1$ and $x = -1$.

Would you like more details on this process or have any questions?

Here are 5 related questions to deepen your understanding:

1. How would you solve $x^2 - 4 = 0$?
2. What happens if the equation was $x^2 + 1 = 0$?
3. How do you solve quadratic equations when they are not factorable?
4. Can you solve $x^2 - 9 = 0$ by factoring?
5. How would you solve a cubic equation like $x^3 - 1 = 0$?

Tip: Always remember to check for both the positive and negative roots when solving $x^2 = c$ equations.