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:

\[ \boxed{\frac{1}{2}} \]