9r^2-18r+4=0

Solution for 9r^2-18r+4=0 equation:

Simplifying
9r2 + -18r + 4 = 0

Reorder the terms:
4 + -18r + 9r2 = 0

Solving
4 + -18r + 9r2 = 0

Solving for variable 'r'.

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

Divide each side by '9'.
0.4444444444 + -2r + r2 = 0

Move the constant term to the right:

Add '-0.4444444444' to each side of the equation.
0.4444444444 + -2r + -0.4444444444 + r2 = 0 + -0.4444444444

Reorder the terms:
0.4444444444 + -0.4444444444 + -2r + r2 = 0 + -0.4444444444

Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000
0.0000000000 + -2r + r2 = 0 + -0.4444444444
-2r + r2 = 0 + -0.4444444444

Combine like terms: 0 + -0.4444444444 = -0.4444444444
-2r + r2 = -0.4444444444

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

Add '1' to each side of the equation.
-2r + 1 + r2 = -0.4444444444 + 1

Reorder the terms:
1 + -2r + r2 = -0.4444444444 + 1

Combine like terms: -0.4444444444 + 1 = 0.5555555556
1 + -2r + r2 = 0.5555555556

Factor a perfect square on the left side:
(r + -1)(r + -1) = 0.5555555556

Calculate the square root of the right side: 0.745355993

Break this problem into two subproblems by setting 
(r + -1) equal to 0.745355993 and -0.745355993.

Subproblem 1
r + -1 = 0.745355993

Simplifying
r + -1 = 0.745355993

Reorder the terms:
-1 + r = 0.745355993

Solving
-1 + r = 0.745355993

Solving for variable 'r'.

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

Add '1' to each side of the equation.
-1 + 1 + r = 0.745355993 + 1

Combine like terms: -1 + 1 = 0
0 + r = 0.745355993 + 1
r = 0.745355993 + 1

Combine like terms: 0.745355993 + 1 = 1.745355993
r = 1.745355993

Simplifying
r = 1.745355993

Subproblem 2
r + -1 = -0.745355993

Simplifying
r + -1 = -0.745355993

Reorder the terms:
-1 + r = -0.745355993

Solving
-1 + r = -0.745355993

Solving for variable 'r'.

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

Add '1' to each side of the equation.
-1 + 1 + r = -0.745355993 + 1

Combine like terms: -1 + 1 = 0
0 + r = -0.745355993 + 1
r = -0.745355993 + 1

Combine like terms: -0.745355993 + 1 = 0.254644007
r = 0.254644007

Simplifying
r = 0.254644007

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.745355993, 0.254644007}