4c^2-8c=1

Solution for 4c^2-8c=1 equation:

Simplifying
4c2 + -8c = 1

Reorder the terms:
-8c + 4c2 = 1

Solving
-8c + 4c2 = 1

Solving for variable 'c'.

Reorder the terms:
-1 + -8c + 4c2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -8c + 4c2 = 0

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

Divide each side by '4'.
-0.25 + -2c + c2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -2c + 0.25 + c2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -2c + c2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -2c + c2 = 0 + 0.25
-2c + c2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-2c + c2 = 0.25

The c term is -2c.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2c + 1 + c2 = 0.25 + 1

Reorder the terms:
1 + -2c + c2 = 0.25 + 1

Combine like terms: 0.25 + 1 = 1.25
1 + -2c + c2 = 1.25

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

Calculate the square root of the right side: 1.118033989

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

Subproblem 1
c + -1 = 1.118033989

Simplifying
c + -1 = 1.118033989

Reorder the terms:
-1 + c = 1.118033989

Solving
-1 + c = 1.118033989

Solving for variable 'c'.

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

Add '1' to each side of the equation.
-1 + 1 + c = 1.118033989 + 1

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

Combine like terms: 1.118033989 + 1 = 2.118033989
c = 2.118033989

Simplifying
c = 2.118033989

Subproblem 2
c + -1 = -1.118033989

Simplifying
c + -1 = -1.118033989

Reorder the terms:
-1 + c = -1.118033989

Solving
-1 + c = -1.118033989

Solving for variable 'c'.

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

Add '1' to each side of the equation.
-1 + 1 + c = -1.118033989 + 1

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

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

Simplifying
c = -0.118033989

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