c^2=4-c

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Solution for c^2=4-c equation: 


Simplifying
c2 = 4 + -1c

Solving
c2 = 4 + -1c

Solving for variable 'c'.

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

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

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

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

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + c + 4 + c2 = 0 + 4

Reorder the terms:
-4 + 4 + c + c2 = 0 + 4

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

Combine like terms: 0 + 4 = 4
c + c2 = 4

The c term is c.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
c + 0.25 + c2 = 4 + 0.25

Reorder the terms:
0.25 + c + c2 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
0.25 + c + c2 = 4.25

Factor a perfect square on the left side:
(c + 0.5)(c + 0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(c + 0.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
c + 0.5 = 2.061552813

Simplifying
c + 0.5 = 2.061552813

Reorder the terms:
0.5 + c = 2.061552813

Solving
0.5 + c = 2.061552813

Solving for variable 'c'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + c = 2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + c = 2.061552813 + -0.5
c = 2.061552813 + -0.5

Combine like terms: 2.061552813 + -0.5 = 1.561552813
c = 1.561552813

Simplifying
c = 1.561552813


Subproblem 2
c + 0.5 = -2.061552813

Simplifying
c + 0.5 = -2.061552813

Reorder the terms:
0.5 + c = -2.061552813

Solving
0.5 + c = -2.061552813

Solving for variable 'c'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + c = -2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + c = -2.061552813 + -0.5
c = -2.061552813 + -0.5

Combine like terms: -2.061552813 + -0.5 = -2.561552813
c = -2.561552813

Simplifying
c = -2.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {1.561552813, -2.561552813}

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