First, subtract #color(red)(2)# from each side of the equation to isolate the radical while keeping the equation balanced:

#sqrt(7k + 2) + 2 - color(red)(2) = 5 - color(red)(2)#

#sqrt(7k + 2) + 0 = 3#

#sqrt(7k + 2) = 3#

Next, square both sides of the equation to eliminate the radical while keeping the equation balanced:

#(sqrt(7k + 2))^2 = 3^2#

#7k + 2 = 9#

Then, subtract #color(red)(2)# from each side of the equation to isolate the #k# term while keeping the equation balanced:

#7k + 2 - color(red)(2) = 9 - color(red)(2)#

#7k + 0 = 7#

#7k = 7#

Now, divide each side of the equation by #color(red)(7)# to solve for #k# while keeping the equation balanced:

#(7k)/color(red)(7) = 7/color(red)(7)#

#(color(red)(cancel(color(black)(7)))k)/cancel(color(red)(7)) = 1#

#k = 1#