Complete the square for the binomial. Then factor the resulting perfect square trinomial.

x^2 -2/11X

To complete the square, add the square of the coefficient of HALF the "x" term.

x^2 - 2/11 x + 1/121
= (x - 1/11)^2

To complete the square for the binomial x^2 - 2/11x, we can follow these steps:

Step 1: Divide the coefficient of the x term by 2 and square the result.
(2/11 / 2)^2 = (1/11)^2 = 1/121

Step 2: Add the result from Step 1 to both sides of the equation.
x^2 - 2/11x + 1/121 = 1/121

Now, we have a perfect square trinomial. To factor it, we can rewrite it as a squared binomial.

(x - 1/11)^2 = 1/121

The binomial (x - 1/11) is the factored form of the resulting perfect square trinomial.

To complete the square for the binomial x^2 -2/11X, we follow these steps:

Step 1: Take half of the coefficient of the x-term and square it.
In this case, the coefficient of the x-term is -2/11. Half of -2/11 is -1/11. Squaring -1/11 gives us (+1/121).

Step 2: Add the squared value to both sides of the equation.
We add +1/121 to both sides of the equation:
x^2 - 2/11X + 1/121 = 1/121

Step 3: Rewrite the equation as a perfect square trinomial.
Now, we can rewrite the left side of our equation as a perfect square trinomial.
(x - 1/11)^2 = 1/121

To factor the resulting perfect square trinomial (x - 1/11)^2, we simply take the square root of both sides of the equation:

√[(x - 1/11)^2] = ± √(1/121)

This gives us two possible solutions:

(x - 1/11) = 1/11 or (x - 1/11) = -1/11

To find the solutions for x, we solve each equation separately:

Equation 1: (x - 1/11) = 1/11
Adding 1/11 to both sides gives us:
x = 1/11 + 1/11
x = 2/11

Equation 2: (x - 1/11) = -1/11
Adding 1/11 to both sides gives us:
x = -1/11 + 1/11
x = 0/11
x = 0

So, the factored form of the resulting perfect square trinomial is: (x - 1/11)^2 = 1/121, and the solutions for x are x = 2/11 and x = 0.