4r^2+8r=1

Solution for 4r^2+8r=1 equation:

Simplifying
4r2 + 8r = 1

Reorder the terms:
8r + 4r2 = 1

Solving
8r + 4r2 = 1

Solving for variable 'r'.

Reorder the terms:
-1 + 8r + 4r2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 8r + 4r2 = 0

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

Divide each side by '4'.
-0.25 + 2r + r2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 2r + 0.25 + r2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 2r + r2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 2r + r2 = 0 + 0.25
2r + r2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
2r + r2 = 0.25

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 = 0.25 + 1

Reorder the terms:
1 + 2r + r2 = 0.25 + 1

Combine like terms: 0.25 + 1 = 1.25
1 + 2r + r2 = 1.25

Factor a perfect square on the left side:
(r + 1)(r + 1) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(r + 1) equal to 1.118033989 and -1.118033989.

Subproblem 1
r + 1 = 1.118033989

Simplifying
r + 1 = 1.118033989

Reorder the terms:
1 + r = 1.118033989

Solving
1 + r = 1.118033989

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 = 1.118033989 + -1

Combine like terms: 1 + -1 = 0
0 + r = 1.118033989 + -1
r = 1.118033989 + -1

Combine like terms: 1.118033989 + -1 = 0.118033989
r = 0.118033989

Simplifying
r = 0.118033989

Subproblem 2
r + 1 = -1.118033989

Simplifying
r + 1 = -1.118033989

Reorder the terms:
1 + r = -1.118033989

Solving
1 + r = -1.118033989

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 = -1.118033989 + -1

Combine like terms: 1 + -1 = 0
0 + r = -1.118033989 + -1
r = -1.118033989 + -1

Combine like terms: -1.118033989 + -1 = -2.118033989
r = -2.118033989

Simplifying
r = -2.118033989

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.118033989, -2.118033989}