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Let's solve the quadratic equation \( x^2 + 2x - 6 = 0 \) by completing the square.

### Step-by-Step Solution:

1. **Start with the quadratic equation**:
   \[
   x^2 + 2x - 6 = 0
   \]

2. **Move the constant term to the right side**:
   \[
   x^2 + 2x = 6
   \]

3. **To complete the square, take half of the coefficient of \(x\)** (which is 2), square it, and add it to both sides:
   \[
   \left(\frac{2}{2}\right)^2 = 1
   \]
   Add 1 to both sides:
   \[
   x^2 + 2x + 1 = 6 + 1
   \]

4. **Now the left side is a perfect square**:
   \[
   (x + 1)^2 = 7
   \]

5. **Take the square root of both sides**:
   \[
   x + 1 = \pm \sqrt{7}
   \]

6. **Solve for \(x\)**:
   \[
   x = -1 \pm \sqrt{7}
   \]

### Final Answer:
\[
x = -1 + \sqrt{7}, \quad x = -1 - \sqrt{7}
\]

To round to the nearest hundredth:

- \( \sqrt{7} \approx 2.65 \)
  
So:

- \( x_1 \approx -1 + 2.65 = 1.65 \)
- \( x_2 \approx -1 - 2.65 = -3.65 \)

### Final Answer Rounded to Nearest Hundredth:
\[
x \approx 1.65, -3.65
\]

Would you like further details on this solution or have any questions?

### Related Questions:
1. How do you solve quadratic equations using the quadratic formula?
2. What are the conditions under which a quadratic equation has real, repeated, or complex solutions?
3. How can you graphically represent the solutions of a quadratic equation?
4. What is the importance of completing the square in deriving the quadratic formula?
5. How does completing the square help in converting a quadratic equation into vertex form?

### Tip:
Completing the square is a useful technique not only for solving quadratic equations but also for deriving the quadratic formula and finding the vertex of a parabola.

Learn how to solve the quadratic equation x^2 + 2x - 6 = 0 by completing the square with a step-by-step solution. This problem covers key algebraic concepts such as quadratic equations and completing the square method. Suitable for high school students (Grades 9-12).

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