Let's solve the quadratic equation $2x^2 + 4x + 2 = 0$ to determine the correct solution.

Step 1: Simplify the quadratic equation

We can divide the entire equation by 2 to make it easier: $x^2 + 2x + 1 = 0$

Step 2: Factor the quadratic equation

Notice that the equation can be factored as: $(x + 1)(x + 1) = 0 \quad \text{or} \quad (x + 1)^2 = 0$

Step 3: Solve for $x$

$x + 1 = 0 \quad \Rightarrow \quad x = -1$

Thus, the only solution is $x = -1$.

Step 4: Verify the roots

Since the root has multiplicity 2, the correct answer corresponds to: $x = -1, \quad x = -1$

Correct Option

The correct answer is the second option:
$x = -1, \quad x = -1$

Do you want further details or explanations?

Here are five related questions to consider:

1. How do you solve a quadratic equation by the quadratic formula?
2. What does it mean if a quadratic equation has a double root?
3. Can all quadratic equations be factored easily?
4. What does the graph of $y = 2x^2 + 4x + 2$ look like?
5. How does the discriminant help determine the number of roots?

Tip: When factoring is tricky, the quadratic formula can always be used to find the roots!