2х²-2x+½=0

To solve the quadratic equation \( 2x^2 - 2x + \frac{1}{2} = 0 \), we can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Here, the coefficients are: - \( a = 2 \) - \( b = -2 \) - \( c = \frac{1}{2} \) First, we will calculate the discriminant \( b^2 - 4ac \): \[ b^2 = (-2)^2 = 4 \] \[ 4ac = 4 \cdot 2 \cdot \frac{1}{2} = 4 \] \[ b^2 - 4ac = 4 - 4 = 0 \] Since the discriminant is 0, there is one real double root. Now we can use the quadratic formula to find the solution: \[ x = \frac{-(-2) \pm \sqrt{0}}{2 \cdot 2} = \frac{2 \pm 0}{4} = \frac{2}{4} = \frac{1}{2} \] Thus, the solution to the equation \( 2x^2 - 2x + \frac{1}{2} = 0 \) is: \[ \boxed{\frac{1}{2}} \]