Quadratic Equation Discriminant Problem

Consider the quadratic equation given by:

$$2x^2 - 4x + k = 0$$

where $k$ is a constant. For the equation to have exactly one real solution, the discriminant must be equal to zero. Recall that the discriminant $D$ of a quadratic equation of the form $ax^2 + bx + c = 0$ is given by:

$$D = b^2 - 4ac$$

Using this information, determine the value of $k$ such that the quadratic equation has exactly one real solution.