Step-by-step explanation:

6a²-4a+(k+1)=0

to make it a perfect square we use,

(b/2a)²=c

where a=6 , b= -4 , c= k+1

substitute we get

(-4/2(6))² = k+1

solving for k

(-1/3)²=k+1

k+1 = 1/9

k= 1/9 - 1

k= -8/9