Complete the square for the binomial. Then factor the resulting perfect square trinomial.
x^2 -2/11X
To complete the square for the binomial x^2 - 2/11x, follow these steps:
1. Take half of the coefficient of the x term and square it. In this case, the coefficient of x is -2/11, so half of it is -2/11 * 1/2 = -1/11, and squaring it gives us (-1/11)^2 = 1/121.
2. Add the square from step 1 to both sides of the equation. We have: x^2 -2/11x + 1/121 = 1/121.
3. Rewriting the left side of the equation as a perfect square trinomial: (x - 1/11)^2 = 1/121.
4. Taking the square root of both sides to solve for x - 1/11: x - 1/11 = ±√(1/121).
5. Simplify the square root of 1/121: √(1/121) = 1/11.
6. Solve for x by adding or subtracting 1/11 from both sides:
x - 1/11 = ± 1/11.
x = 1/11 ± 1/11.
Finally, we can factor the resulting perfect square trinomial: (x - 1/11)^2 = 1/121 can be factored as (x - 1/11)(x - 1/11) = 1/121.