C^2-C^0-2C=0

Solution for C^2-C^0-2C=0 equation:

Simplifying
C2 + -1C0 + -2C = 0

Reorder the terms:
-1 + -2C + C2 = 0

Solving
-1 + -2C + C2 = 0

Solving for variable 'C'.

Begin completing the square.

Move the constant term to the right:

Add '' to each side of the equation.
-1 + -2C +  + C2 = 0 + 

Reorder the terms:
-1 +  + -2C + C2 = 0 + 

Combine like terms: -1 +  = 0
0 + -2C + C2 = 0 + 
-2C + C2 = 0 + 

Combine like terms: 0 +  = 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}