Root

By vieta's formula; sum of roots= $8$
Since, equation possesses one root; this means that in fact, both roots are equal or both roots are $\frac {8}{2}=4$

To have only one root, the equation $Ax^2 + Bx + C = 0$ must be a perfect square. That is, $B^2 = 4AC$

From the problem,

$B = -8$

$A = 1$

$C = k$

Substituting, we get

$(-8)^2 = 4(1)(k)$

$64 = 4k$

$k = 16$

Solving for $x$ , we get

$x^2 - 8x + 16 = 0$

$(x - 4)^2 = 0$

$\boxed{x = 4}$