First, subtract #color(red)(7)# from each side of the equation to isolate the square root expression while keeping the equation balanced:

#-color(red)(7) + 7 - sqrt(x - 6) = -color(red)(7) + 3#

#0 - sqrt(x - 6) = -4#

#-sqrt(x - 6) = -4#

Next, multiply each side of the equation by #color(red)(-1)# to eliminate the negative terms while keeping the equation balanced:

#color(red)(-1) xx -sqrt(x - 6) = color(red)(-1) xx -4#

#sqrt(x - 6) = 4#

Then, square both sides of the equation to eliminate the square root function while keeping the equation balanced:

#(sqrt(x - 6))^2 = 4^2#

#x - 6 = 16#

Now, add #color(red)(6)# to each side of the equation to solve for #x# while keeping the equation balanced:

#x - 6 + color(red)(6) = 16 + color(red)(6)#

#x - 0 = 22#

#x = 22#

An extraneous solution would be #sqrt(x - 6) = -4#