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The image presents the following quadratic equation to be solved using both the methods of "completing the square" and the "quadratic formula":

\[
2x^2 - 4x - 6 = 0
\]

Let's first solve this using both methods:

### 1. **Completing the Square Method:**

Step 1: Start with the original equation:
\[
2x^2 - 4x - 6 = 0
\]

Step 2: Divide the entire equation by 2 to simplify:
\[
x^2 - 2x - 3 = 0
\]

Step 3: Move the constant term (-3) to the right side:
\[
x^2 - 2x = 3
\]

Step 4: To complete the square, take half of the coefficient of \(x\), square it, and add it to both sides:
\[
\left( \frac{-2}{2} \right)^2 = 1
\]
Add 1 to both sides:
\[
x^2 - 2x + 1 = 3 + 1
\]
\[
(x - 1)^2 = 4
\]

Step 5: Take the square root of both sides:
\[
x - 1 = \pm 2
\]

Step 6: Solve for \(x\):
\[
x = 1 \pm 2
\]
Thus, \(x = 3\) or \(x = -1\).

### 2. **Quadratic Formula Method:**

The quadratic formula is given by:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
For the equation \(2x^2 - 4x - 6 = 0\), the coefficients are:
- \(a = 2\)
- \(b = -4\)
- \(c = -6\)

Substitute these values into the quadratic formula:
\[
x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(2)(-6)}}{2(2)}
\]
\[
x = \frac{4 \pm \sqrt{16 + 48}}{4}
\]
\[
x = \frac{4 \pm \sqrt{64}}{4}
\]
\[
x = \frac{4 \pm 8}{4}
\]

This gives two solutions:
\[
x = \frac{4 + 8}{4} = 3 \quad \text{or} \quad x = \frac{4 - 8}{4} = -1
\]

### Final Answer:
The solutions are \(x = 3\) and \(x = -1\), which are the same using both methods.

---

Do you have any questions about the process or would you like further details?

### Related Questions:
1. What are the advantages of using the quadratic formula over completing the square?
2. Can completing the square be used for any quadratic equation?
3. How does the discriminant in the quadratic formula affect the number of solutions?
4. What are the key steps to avoid mistakes when using the quadratic formula?
5. How can you apply completing the square to solve equations in real-life scenarios?

**Tip:** When using the quadratic formula, always calculate the discriminant (\(b^2 - 4ac\)) first to check if the roots are real or complex.

Solve the quadratic equation 2x^2 - 4x - 6 = 0 using completing the square and quadratic formula.

Learn how to solve the quadratic equation 2x^2 - 4x - 6 = 0 using both completing the square and quadratic formula methods. This step-by-step solution covers important algebraic concepts for students in Grades 9-10.

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