2c+1=c^2

Solution for 2c+1=c^2 equation:

Simplifying
2c + 1 = c2

Reorder the terms:
1 + 2c = c2

Solving
1 + 2c = c2

Solving for variable 'c'.

Combine like terms: c2 + -1c2 = 0
1 + 2c + -1c2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + -2c + c2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2c + 1 + c2 = 0 + 1

Reorder the terms:
-1 + 1 + -2c + c2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2c + c2 = 0 + 1
-2c + c2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2c + c2 = 1

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 = 1 + 1

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

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

Factor a perfect square on the left side:
(c + -1)(c + -1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(c + -1) equal to 1.414213562 and -1.414213562.

Subproblem 1
c + -1 = 1.414213562

Simplifying
c + -1 = 1.414213562

Reorder the terms:
-1 + c = 1.414213562

Solving
-1 + c = 1.414213562

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 = 1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + c = 1.414213562 + 1
c = 1.414213562 + 1

Combine like terms: 1.414213562 + 1 = 2.414213562
c = 2.414213562

Simplifying
c = 2.414213562

Subproblem 2
c + -1 = -1.414213562

Simplifying
c + -1 = -1.414213562

Reorder the terms:
-1 + c = -1.414213562

Solving
-1 + c = -1.414213562

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 = -1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + c = -1.414213562 + 1
c = -1.414213562 + 1

Combine like terms: -1.414213562 + 1 = -0.414213562
c = -0.414213562

Simplifying
c = -0.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {2.414213562, -0.414213562}