To solve the quadratic equation $x^2 - 4x + 2 = 0$, we can use the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

For this equation, we have:

• $a = 1$
• $b = -4$
• $c = 2$

Step 1: Substitute values into the formula

$x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4 \cdot 1 \cdot 2}}{2 \cdot 1}$

Step 2: Simplify inside the square root

$x = \frac{4 \pm \sqrt{16 - 8}}{2}$

Step 3: Simplify further

$x = \frac{4 \pm \sqrt{8}}{2}$

Step 4: Simplify $\sqrt{8}$ as $2\sqrt{2}$

$x = \frac{4 \pm 2\sqrt{2}}{2}$

Step 5: Divide by 2

$x = 2 \pm \sqrt{2}$

Final Answer

The solutions are: $x = 2 + \sqrt{2} \quad \text{and} \quad x = 2 - \sqrt{2}$

Would you like further details or have any questions?

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Here are 5 related questions:

1. How can we verify the solutions of a quadratic equation?
2. What are the possible methods for solving quadratic equations other than the quadratic formula?
3. How does the discriminant (inside the square root) affect the nature of the solutions?
4. What are real-world applications where quadratic equations are commonly used?
5. How do you solve a quadratic equation by completing the square?

Tip: Always check your solutions by substituting them back into the original equation!