What number must you add to complete the square x^2+8x=11

x^2+8x=11

Take half of the coefficient (8) of x and square it.  Result:  16.

x^2+8x=11      Add 16 to x^2+8x, and then subtract 64 from the result:

x^2 + 8x + 16 - 16 = 11
Recognize that the first 3 terms can be rewritten as (x+4)^2.

Then:

  (x+4)^2 - 16 = 11, or (x+4)^2 = 27

  Add 16, and then subtract 16, as shown.

Solve for x?  find the sqrt of both sides:  x+4 = plus or minus 3sqrt(3)

Then x = -4 plus or minus 3sqrt(3)