Finding k in a Quadratic Equation

Consider the quadratic equation given by:

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

where $$k$$ is a constant. The equation has exactly one solution when $$k$$ is set to a certain value. Determine the value of $$k$$ that makes the equation have exactly one solution, then calculate the value of $$x$$ when $$k$$ is at that value.