To solve the quadratic equation \( x^2 - x - 2 = 0 \), we can use either factoring or the quadratic formula. Let's solve it by factoring first.

We need to find two numbers that multiply to \(-2\) (the constant term) and add to \(-1\) (the coefficient of \(x\)).

The numbers \(-2\) and \(1\) satisfy this condition:

\[
x^2 - x - 2 = (x - 2)(x + 1) = 0
\]

Now, set each factor equal to zero:

\[
x - 2 = 0 \quad \text{or} \quad x + 1 = 0
\]

Solving these:

\[
x = 2 \quad \text{or} \quad x = -1
\]

So, the solutions to the equation \( x^2 - x - 2 = 0 \) are:

\[
x = 2 \quad \text{or} \quad x = -1
\]

Would you like further details or have any questions?

Here are some related questions:
1. How can you confirm the solutions by substituting back into the original equation?
2. What if the quadratic equation does not factor easily? How can you solve it then?
3. What is the geometric interpretation of the solutions to a quadratic equation?
4. How would you use the quadratic formula to solve \(x^2 - x - 2 = 0\)?
5. How can completing the square be applied to solve this equation?

**Tip:** Always check your solutions by substituting them back into the original equation to ensure they satisfy it.

Learn how to solve the quadratic equation x^2 - x - 2 with a detailed step-by-step solution using factoring and the quadratic formula. Explore the concepts of algebra, factoring, and quadratic equations. Suitable for students in Grades 7-9.

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