To solve the equation \( 2x^2 - x - 1 = -1 \), follow these steps:

1. **Simplify the equation**: Add 1 to both sides to eliminate the \(-1\) on the right side.
   \[
   2x^2 - x - 1 + 1 = -1 + 1
   \]
   This simplifies to:
   \[
   2x^2 - x = 0
   \]

2. **Factor the equation**: Factor out the common term \(x\) from the left side.
   \[
   x(2x - 1) = 0
   \]

3. **Solve for \(x\)**: Set each factor equal to 0 and solve for \(x\).
   \[
   x = 0
   \]
   \[
   2x - 1 = 0
   \]
   Solving the second equation:
   \[
   2x = 1
   \]
   \[
   x = \frac{1}{2}
   \]

So, the solutions are \( x = 0 \) and \( x = \frac{1}{2} \).

Would you like a detailed explanation of any of these steps or have any questions?

Here are 5 related questions you might find interesting:

1. How would you solve the equation \(3x^2 - 9x + 6 = 0\)?
2. What are the solutions to the equation \(x^2 - 4x + 4 = 0\)?
3. How can you factor the quadratic expression \(x^2 + 5x + 6\)?
4. What are the steps to solve the equation \(4x^2 + 4x - 3 = 0\) using the quadratic formula?
5. How do you complete the square for the quadratic equation \(x^2 + 6x + 5 = 0\)?

**Tip:** When factoring quadratic equations, always look for common factors first, as it can simplify the process significantly.

Discover how to solve the quadratic equation 2x^2 - x - 1 = -1 with a clear step-by-step guide. This problem involves algebraic concepts such as simplifying, factoring, and applying the Zero Product Property. Ideal for students in Grades 8-10.

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