We have the equation:

\[
x^2 - 2x - 5 = -5
\]

### Step 1: Move all terms to one side of the equation.
Add \(5\) to both sides to simplify:

\[
x^2 - 2x - 5 + 5 = -5 + 5
\]

This simplifies to:

\[
x^2 - 2x = 0
\]

### Step 2: Factor the equation.
Factor out \(x\):

\[
x(x - 2) = 0
\]

### Step 3: Solve for \(x\).
For the product to be zero, either \(x = 0\) or \(x - 2 = 0\).

- If \(x = 0\), that’s one solution.
- If \(x - 2 = 0\), solve for \(x\):

\[
x = 2
\]

### Final Answer:
The solutions are \(x = 0\) and \(x = 2\).

Would you like more details or have any questions?

Here are five related questions:
1. How do you solve quadratic equations using factoring?
2. What if the equation can't be factored easily?
3. How does the quadratic formula work?
4. What are the key differences between factoring and completing the square?
5. Can you explain how to check solutions in quadratic equations?

**Tip:** Always check both solutions by substituting them back into the original equation to ensure they are correct.

Learn how to solve the quadratic equation x^2 - 2x - 5 = -5 using factoring. This step-by-step guide simplifies the equation and applies the Zero Product Property to find the solutions x = 0 and x = 2. Suitable for students in Grades 8-10.

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