Possible............

Any quadratic equations with two roots, $a$ and $b$ can be expressed as, $( x - a ) ( x - b) = 0$ . In expansion, it takes the form of $x^2 + (a+b)x - ab = 0$ .
Sum of roots = -( coefficient of x in expanded form )
So, $x( x - k) = k + 1$ $x^2 - kx - (k +1) = 0$

Hence, $-(- k ) = k$

Ans is $k$

Simplifying, we get x^2-kx-k-1. Using vietas formula, we know that the sum of the roots is equal to = -b/a where b in this case -k and a is 1. So the sum is simply k.

x(x-k) = k+1 => x^2 - xk - k - 1 = 0 => (x + 1 ) ( x - 1 ) - k ( x + 1 ) = 0 => (x + 1 ) ( x - 1 - k ) = 0 Either x = - 1 or x = 1 +k So, the sum of all possible solutions is k