How do you solve by completing the square: #x^2 4x11=0#?
1 Answer

First, we Transpose the Constant to one side of the equation.
Transposing#11# to the other side we get:
#x^24x = 11# 
Application of
#(ab)^2 = a^2  2ab + b^2#
We look at the Coefficient of#x# . It's#4#
We take half of this number (including the sign), giving us#–2#
We square this value to get#(2)^2 = 4# . We add this number to BOTH sides of the Equation.
#x^24x+4 = 11+4#
#x^24x+4 = 15#
The Left Hand side#x^24x+4# is in the form#a^2  2ab + b^2#
where#a# is#x# , and#b# is#2# 
The equation can be written as
#(x2)^2 = 15#
So

Solution :
#x = 2+sqrt15,2sqrt15# 
Verify your answer by substituting these values in the Original Equation
#x^2 4x  11 = 0#
You will see that the Solution is correct.