First, add #color(red)(8)# to each side of the equation to isolate the radical term while keeping the equation balanced:
#2sqrt(x - 11) - 8 + color(red)(8) = 4 + color(red)(8)#
#2sqrt(x - 11) - 0 = 12#
#2sqrt(x - 11) = 12#
Next, divide each side of the equation by #color(red)(2)# to isolate the radical while keeping the equation balanced:
#(2sqrt(x - 11))/color(red)(2) = 12/color(red)(2)#
#(color(red)(cancel(color(black)(2)))sqrt(x - 11))/cancel(color(red)(2)) = 6#
#sqrt(x - 11) = 6#
Then square each side of the equation to eliminate the radical while keeping the equation balanced:
#(sqrt(x - 11))^2 = 6^2#
#x - 11 = 36#
Now, add #color(red)(11)# to each side of the equation to solve for #x# while keeping the equation balanced:
#x - 11 + color(red)(11) = 36 + color(red)(11)#
#x - 0 = 47#
#x = 47#
To check the solution substitute #color(red)(47)# for #color(red)(x)# in the original equation and calculate the left side of the equation to ensure it equals #4#
#2sqrt(color(red)(x) - 11) - 8 = 4# becomes:
#2sqrt(color(red)(47) - 11) - 8 = 4#
#2sqrt(36) - 8 = 4#
#(2 xx +-6) - 8 = 4#
#+-12 - 8 = 4#
#4 = 4#
Or
#-20 != 4#
The solution of #-20# is extraneous.
