What number must you add to complete the square? x2 8x = 11

 let the number be k 
so x^2+8x+K=11+k 
k=(coefficent of x/2)^2=8/2=4^2=16 
so x^2+8x+16=11+16 
(x+4)^2=27 

x+4=+-root of 27 
x=4+root of 27 or 4-root of 27