r^2-16r+6=0

Solution for r^2-16r+6=0 equation:

Simplifying
r2 + -16r + 6 = 0

Reorder the terms:
6 + -16r + r2 = 0

Solving
6 + -16r + 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 + -16r + -6 + r2 = 0 + -6

Reorder the terms:
6 + -6 + -16r + r2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -16r + r2 = 0 + -6
-16r + r2 = 0 + -6

Combine like terms: 0 + -6 = -6
-16r + r2 = -6

The r term is -16r.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16r + 64 + r2 = -6 + 64

Reorder the terms:
64 + -16r + r2 = -6 + 64

Combine like terms: -6 + 64 = 58
64 + -16r + r2 = 58

Factor a perfect square on the left side:
(r + -8)(r + -8) = 58

Calculate the square root of the right side: 7.615773106

Break this problem into two subproblems by setting 
(r + -8) equal to 7.615773106 and -7.615773106.

Subproblem 1
r + -8 = 7.615773106

Simplifying
r + -8 = 7.615773106

Reorder the terms:
-8 + r = 7.615773106

Solving
-8 + r = 7.615773106

Solving for variable 'r'.

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

Add '8' to each side of the equation.
-8 + 8 + r = 7.615773106 + 8

Combine like terms: -8 + 8 = 0
0 + r = 7.615773106 + 8
r = 7.615773106 + 8

Combine like terms: 7.615773106 + 8 = 15.615773106
r = 15.615773106

Simplifying
r = 15.615773106

Subproblem 2
r + -8 = -7.615773106

Simplifying
r + -8 = -7.615773106

Reorder the terms:
-8 + r = -7.615773106

Solving
-8 + r = -7.615773106

Solving for variable 'r'.

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

Add '8' to each side of the equation.
-8 + 8 + r = -7.615773106 + 8

Combine like terms: -8 + 8 = 0
0 + r = -7.615773106 + 8
r = -7.615773106 + 8

Combine like terms: -7.615773106 + 8 = 0.384226894
r = 0.384226894

Simplifying
r = 0.384226894

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {15.615773106, 0.384226894}