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

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

To complete the square and solve for x , for the given equation the following has to be done.

x^2 - 8x - 11 = 0

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

Now we have a square on the left

=> (x - 4)^2 = 27

=> (x - 4)^2 = (sqrt 27)^2

Now we have squares on both the sides.

=> x - 4 = sqrt 27 and x - 4 = -sqrt 27

=> x = 4 + sqrt 27 and x = 4 - sqrt 27

The solution of the equation is x = 4 + sqrt 27 and x = 4 - sqrt 27

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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}.