What does it mean "Complete the square and solve for x"? x^2-8x-11=0

It means that we'll not apply the quadratic formula or
factorization to solve the quadratic.

Let's see how we'll
do it.

For the beginning, we'll add 11 to both sides,
to move the constant to the right side of the equation, so that being more clear what
we have to do to the left side to complete the square.

x^2
- 8x = 11

We'll complete the square by adding the number 16
both sides, to get a perfect square to the left side.

x^2-
8x + 16 =11+16

We'll write the left side as a perfect
square:

(x - 4)^2 = 27

We'll
take square root both sides:

x - 4 = +-sqrt
27

x - 4 = +-3sqrt3

x1 = 4 +
3*sqrt 3

x2 = 4 - 3*sqrt
3

The solutions of the equation are: { 4 -
3*sqrt 3 ; 4 + 3*sqrt 3}.