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The given quadratic equation is:

\[
x^2 - 1 = 0
\]

We can solve this by factoring. The expression \(x^2 - 1\) is a difference of squares, which factors as:

\[
x^2 - 1 = (x - 1)(x + 1)
\]

Now, set each factor equal to zero:

\[
x - 1 = 0 \quad \text{or} \quad x + 1 = 0
\]

Solving both equations:

1. \(x - 1 = 0 \implies x = 1\)
2. \(x + 1 = 0 \implies x = -1\)

Thus, the solutions are:

\[
x = 1 \quad \text{and} \quad x = -1
\]

Would you like more details or have any questions?

Here are 5 related questions you might find helpful:
1. How do you factor other types of quadratic equations?
2. What is the method for solving quadratics when factoring is not possible?
3. Can the quadratic formula be used as an alternative to factoring?
4. How does the difference of squares factoring method work in general?
5. What are other special factorable forms besides the difference of squares?

**Tip**: Whenever you see an expression like \(a^2 - b^2\), always check if it can be factored using the difference of squares method!

Give the solutions for x for each of the following Secondary (Quadratic) equations: x^2 - 1 = 0

Learn how to solve the quadratic equation x^2 - 1 = 0 using the factoring method. This solution applies the difference of squares theorem, breaking down the equation into (x - 1)(x + 1) = 0. Suitable for students in Grades 7-9.

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