X^2-4x+2=0

To solve the quadratic equation \( x^2 - 4x + 2 = 0 \), we can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] where \( a = 1 \), \( b = -4 \), and \( c = 2 \). **Step-by-step solution:** 1. **Identify coefficients:** \[ a = 1, \quad b = -4, \quad c = 2 \] 2. **Calculate the discriminant:** \[ D = b^2 - 4ac = (-4)^2 - 4 \times 1 \times 2 = 16 - 8 = 8 \] 3. **Compute the square root of the discriminant:** \[ \sqrt{D} = \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2} \] 4. **Apply the quadratic formula:** \[ x = \frac{-(-4) \pm 2\sqrt{2}}{2 \times 1} = \frac{4 \pm 2\sqrt{2}}{2} \] 5. **Simplify:** \[ x = 2 \pm \sqrt{2} \] **Final answer:** \[ \boxed{ x = 2 + \sqrt{2} \quad \text{or} \quad x = 2 - \sqrt{2} } \] These are the solutions to the quadratic equation.