r^2-9r+6=

Solution for r^2-9r+6= equation:

Simplifying
r2 + -9r + 6 = 0

Reorder the terms:
6 + -9r + r2 = 0

Solving
6 + -9r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -9r + -6 + r2 = 0 + -6

Reorder the terms:
6 + -6 + -9r + r2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -9r + r2 = 0 + -6
-9r + r2 = 0 + -6

Combine like terms: 0 + -6 = -6
-9r + r2 = -6

The r term is -9r.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9r + 20.25 + r2 = -6 + 20.25

Reorder the terms:
20.25 + -9r + r2 = -6 + 20.25

Combine like terms: -6 + 20.25 = 14.25
20.25 + -9r + r2 = 14.25

Factor a perfect square on the left side:
(r + -4.5)(r + -4.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(r + -4.5) equal to 3.774917218 and -3.774917218.

Subproblem 1
r + -4.5 = 3.774917218

Simplifying
r + -4.5 = 3.774917218

Reorder the terms:
-4.5 + r = 3.774917218

Solving
-4.5 + r = 3.774917218

Solving for variable 'r'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + r = 3.774917218 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + r = 3.774917218 + 4.5
r = 3.774917218 + 4.5

Combine like terms: 3.774917218 + 4.5 = 8.274917218
r = 8.274917218

Simplifying
r = 8.274917218

Subproblem 2
r + -4.5 = -3.774917218

Simplifying
r + -4.5 = -3.774917218

Reorder the terms:
-4.5 + r = -3.774917218

Solving
-4.5 + r = -3.774917218

Solving for variable 'r'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + r = -3.774917218 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + r = -3.774917218 + 4.5
r = -3.774917218 + 4.5

Combine like terms: -3.774917218 + 4.5 = 0.725082782
r = 0.725082782

Simplifying
r = 0.725082782

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {8.274917218, 0.725082782}