9u^2-18u+2=0

Solution for 9u^2-18u+2=0 equation:

Simplifying
9u2 + -18u + 2 = 0

Reorder the terms:
2 + -18u + 9u2 = 0

Solving
2 + -18u + 9u2 = 0

Solving for variable 'u'.

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
0.2222222222 + -2u + u2 = 0

Move the constant term to the right:

Add '-0.2222222222' to each side of the equation.
0.2222222222 + -2u + -0.2222222222 + u2 = 0 + -0.2222222222

Reorder the terms:
0.2222222222 + -0.2222222222 + -2u + u2 = 0 + -0.2222222222

Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000
0.0000000000 + -2u + u2 = 0 + -0.2222222222
-2u + u2 = 0 + -0.2222222222

Combine like terms: 0 + -0.2222222222 = -0.2222222222
-2u + u2 = -0.2222222222

The u term is -2u.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2u + 1 + u2 = -0.2222222222 + 1

Reorder the terms:
1 + -2u + u2 = -0.2222222222 + 1

Combine like terms: -0.2222222222 + 1 = 0.7777777778
1 + -2u + u2 = 0.7777777778

Factor a perfect square on the left side:
(u + -1)(u + -1) = 0.7777777778

Calculate the square root of the right side: 0.881917104

Break this problem into two subproblems by setting 
(u + -1) equal to 0.881917104 and -0.881917104.

Subproblem 1
u + -1 = 0.881917104

Simplifying
u + -1 = 0.881917104

Reorder the terms:
-1 + u = 0.881917104

Solving
-1 + u = 0.881917104

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + u = 0.881917104 + 1

Combine like terms: -1 + 1 = 0
0 + u = 0.881917104 + 1
u = 0.881917104 + 1

Combine like terms: 0.881917104 + 1 = 1.881917104
u = 1.881917104

Simplifying
u = 1.881917104

Subproblem 2
u + -1 = -0.881917104

Simplifying
u + -1 = -0.881917104

Reorder the terms:
-1 + u = -0.881917104

Solving
-1 + u = -0.881917104

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + u = -0.881917104 + 1

Combine like terms: -1 + 1 = 0
0 + u = -0.881917104 + 1
u = -0.881917104 + 1

Combine like terms: -0.881917104 + 1 = 0.118082896
u = 0.118082896

Simplifying
u = 0.118082896

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {1.881917104, 0.118082896}