r^2-10r+6=0

Solution for r^2-10r+6=0 equation:

Simplifying
r2 + -10r + 6 = 0

Reorder the terms:
6 + -10r + r2 = 0

Solving
6 + -10r + 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 + -10r + -6 + r2 = 0 + -6

Reorder the terms:
6 + -6 + -10r + r2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -10r + r2 = 0 + -6
-10r + r2 = 0 + -6

Combine like terms: 0 + -6 = -6
-10r + r2 = -6

The r term is -10r.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10r + 25 + r2 = -6 + 25

Reorder the terms:
25 + -10r + r2 = -6 + 25

Combine like terms: -6 + 25 = 19
25 + -10r + r2 = 19

Factor a perfect square on the left side:
(r + -5)(r + -5) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(r + -5) equal to 4.358898944 and -4.358898944.

Subproblem 1
r + -5 = 4.358898944

Simplifying
r + -5 = 4.358898944

Reorder the terms:
-5 + r = 4.358898944

Solving
-5 + r = 4.358898944

Solving for variable 'r'.

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

Add '5' to each side of the equation.
-5 + 5 + r = 4.358898944 + 5

Combine like terms: -5 + 5 = 0
0 + r = 4.358898944 + 5
r = 4.358898944 + 5

Combine like terms: 4.358898944 + 5 = 9.358898944
r = 9.358898944

Simplifying
r = 9.358898944

Subproblem 2
r + -5 = -4.358898944

Simplifying
r + -5 = -4.358898944

Reorder the terms:
-5 + r = -4.358898944

Solving
-5 + r = -4.358898944

Solving for variable 'r'.

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

Add '5' to each side of the equation.
-5 + 5 + r = -4.358898944 + 5

Combine like terms: -5 + 5 = 0
0 + r = -4.358898944 + 5
r = -4.358898944 + 5

Combine like terms: -4.358898944 + 5 = 0.641101056
r = 0.641101056

Simplifying
r = 0.641101056

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {9.358898944, 0.641101056}