8r^2-16r+7=0

Solution for 8r^2-16r+7=0 equation:

Simplifying
8r2 + -16r + 7 = 0

Reorder the terms:
7 + -16r + 8r2 = 0

Solving
7 + -16r + 8r2 = 0

Solving for variable 'r'.

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

Divide each side by '8'.
0.875 + -2r + r2 = 0

Move the constant term to the right:

Add '-0.875' to each side of the equation.
0.875 + -2r + -0.875 + r2 = 0 + -0.875

Reorder the terms:
0.875 + -0.875 + -2r + r2 = 0 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + -2r + r2 = 0 + -0.875
-2r + r2 = 0 + -0.875

Combine like terms: 0 + -0.875 = -0.875
-2r + r2 = -0.875

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 = -0.875 + 1

Reorder the terms:
1 + -2r + r2 = -0.875 + 1

Combine like terms: -0.875 + 1 = 0.125
1 + -2r + r2 = 0.125

Factor a perfect square on the left side:
(r + -1)(r + -1) = 0.125

Calculate the square root of the right side: 0.353553391

Break this problem into two subproblems by setting 
(r + -1) equal to 0.353553391 and -0.353553391.

Subproblem 1
r + -1 = 0.353553391

Simplifying
r + -1 = 0.353553391

Reorder the terms:
-1 + r = 0.353553391

Solving
-1 + r = 0.353553391

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 = 0.353553391 + 1

Combine like terms: -1 + 1 = 0
0 + r = 0.353553391 + 1
r = 0.353553391 + 1

Combine like terms: 0.353553391 + 1 = 1.353553391
r = 1.353553391

Simplifying
r = 1.353553391

Subproblem 2
r + -1 = -0.353553391

Simplifying
r + -1 = -0.353553391

Reorder the terms:
-1 + r = -0.353553391

Solving
-1 + r = -0.353553391

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 = -0.353553391 + 1

Combine like terms: -1 + 1 = 0
0 + r = -0.353553391 + 1
r = -0.353553391 + 1

Combine like terms: -0.353553391 + 1 = 0.646446609
r = 0.646446609

Simplifying
r = 0.646446609

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.353553391, 0.646446609}