4(c+4)c=4

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Solution for 4(c+4)c=4 equation: 


Simplifying
4(c + 4) * c = 4

Reorder the terms:
4(4 + c) * c = 4

Reorder the terms for easier multiplication:
4c(4 + c) = 4
(4 * 4c + c * 4c) = 4
(16c + 4c2) = 4

Solving
16c + 4c2 = 4

Solving for variable 'c'.

Reorder the terms:
-4 + 16c + 4c2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 16c + 4c2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 4c + c2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1 + 4c + c2)' equal to zero and attempt to solve:

Simplifying
-1 + 4c + c2 = 0

Solving
-1 + 4c + c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 4c + 1 + c2 = 0 + 1

Reorder the terms:
-1 + 1 + 4c + c2 = 0 + 1

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

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

The c term is 4c.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4c + 4 + c2 = 1 + 4

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

Combine like terms: 1 + 4 = 5
4 + 4c + c2 = 5

Factor a perfect square on the left side:
(c + 2)(c + 2) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(c + 2) equal to 2.236067978 and -2.236067978.


Subproblem 1
c + 2 = 2.236067978

Simplifying
c + 2 = 2.236067978

Reorder the terms:
2 + c = 2.236067978

Solving
2 + c = 2.236067978

Solving for variable 'c'.

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

Add '-2' to each side of the equation.
2 + -2 + c = 2.236067978 + -2

Combine like terms: 2 + -2 = 0
0 + c = 2.236067978 + -2
c = 2.236067978 + -2

Combine like terms: 2.236067978 + -2 = 0.236067978
c = 0.236067978

Simplifying
c = 0.236067978


Subproblem 2
c + 2 = -2.236067978

Simplifying
c + 2 = -2.236067978

Reorder the terms:
2 + c = -2.236067978

Solving
2 + c = -2.236067978

Solving for variable 'c'.

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

Add '-2' to each side of the equation.
2 + -2 + c = -2.236067978 + -2

Combine like terms: 2 + -2 = 0
0 + c = -2.236067978 + -2
c = -2.236067978 + -2

Combine like terms: -2.236067978 + -2 = -4.236067978
c = -4.236067978

Simplifying
c = -4.236067978


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.236067978, -4.236067978}
Solution
c = {0.236067978, -4.236067978}

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