c+(c+2)+c(c+4)=27

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Solution for c+(c+2)+c(c+4)=27 equation:


Simplifying
c + (c + 2) + c(c + 4) = 27

Reorder the terms:
c + (2 + c) + c(c + 4) = 27

Remove parenthesis around (2 + c)
c + 2 + c + c(c + 4) = 27

Reorder the terms:
c + 2 + c + c(4 + c) = 27
c + 2 + c + (4 * c + c * c) = 27
c + 2 + c + (4c + c2) = 27

Reorder the terms:
2 + c + c + 4c + c2 = 27

Combine like terms: c + c = 2c
2 + 2c + 4c + c2 = 27

Combine like terms: 2c + 4c = 6c
2 + 6c + c2 = 27

Solving
2 + 6c + c2 = 27

Solving for variable 'c'.

Reorder the terms:
2 + -27 + 6c + c2 = 27 + -27

Combine like terms: 2 + -27 = -25
-25 + 6c + c2 = 27 + -27

Combine like terms: 27 + -27 = 0
-25 + 6c + c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 6c + 25 + c2 = 0 + 25

Reorder the terms:
-25 + 25 + 6c + c2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 6c + c2 = 0 + 25
6c + c2 = 0 + 25

Combine like terms: 0 + 25 = 25
6c + c2 = 25

The c term is 6c.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6c + 9 + c2 = 25 + 9

Reorder the terms:
9 + 6c + c2 = 25 + 9

Combine like terms: 25 + 9 = 34
9 + 6c + c2 = 34

Factor a perfect square on the left side:
(c + 3)(c + 3) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(c + 3) equal to 5.830951895 and -5.830951895.

Subproblem 1

c + 3 = 5.830951895 Simplifying c + 3 = 5.830951895 Reorder the terms: 3 + c = 5.830951895 Solving 3 + c = 5.830951895 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + c = 5.830951895 + -3 Combine like terms: 3 + -3 = 0 0 + c = 5.830951895 + -3 c = 5.830951895 + -3 Combine like terms: 5.830951895 + -3 = 2.830951895 c = 2.830951895 Simplifying c = 2.830951895

Subproblem 2

c + 3 = -5.830951895 Simplifying c + 3 = -5.830951895 Reorder the terms: 3 + c = -5.830951895 Solving 3 + c = -5.830951895 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + c = -5.830951895 + -3 Combine like terms: 3 + -3 = 0 0 + c = -5.830951895 + -3 c = -5.830951895 + -3 Combine like terms: -5.830951895 + -3 = -8.830951895 c = -8.830951895 Simplifying c = -8.830951895

Solution

The solution to the problem is based on the solutions from the subproblems. c = {2.830951895, -8.830951895}

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