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#
