8(c+2)c=5

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Solution for 8(c+2)c=5 equation:


Simplifying
8(c + 2) * c = 5

Reorder the terms:
8(2 + c) * c = 5

Reorder the terms for easier multiplication:
8c(2 + c) = 5
(2 * 8c + c * 8c) = 5
(16c + 8c2) = 5

Solving
16c + 8c2 = 5

Solving for variable 'c'.

Reorder the terms:
-5 + 16c + 8c2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 16c + 8c2 = 0

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

Divide each side by '8'.
-0.625 + 2c + c2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + 2c + 0.625 + c2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + 2c + c2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + 2c + c2 = 0 + 0.625
2c + c2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
2c + c2 = 0.625

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 = 0.625 + 1

Reorder the terms:
1 + 2c + c2 = 0.625 + 1

Combine like terms: 0.625 + 1 = 1.625
1 + 2c + c2 = 1.625

Factor a perfect square on the left side:
(c + 1)(c + 1) = 1.625

Calculate the square root of the right side: 1.274754878

Break this problem into two subproblems by setting 
(c + 1) equal to 1.274754878 and -1.274754878.

Subproblem 1

c + 1 = 1.274754878 Simplifying c + 1 = 1.274754878 Reorder the terms: 1 + c = 1.274754878 Solving 1 + c = 1.274754878 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 = 1.274754878 + -1 Combine like terms: 1 + -1 = 0 0 + c = 1.274754878 + -1 c = 1.274754878 + -1 Combine like terms: 1.274754878 + -1 = 0.274754878 c = 0.274754878 Simplifying c = 0.274754878

Subproblem 2

c + 1 = -1.274754878 Simplifying c + 1 = -1.274754878 Reorder the terms: 1 + c = -1.274754878 Solving 1 + c = -1.274754878 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 = -1.274754878 + -1 Combine like terms: 1 + -1 = 0 0 + c = -1.274754878 + -1 c = -1.274754878 + -1 Combine like terms: -1.274754878 + -1 = -2.274754878 c = -2.274754878 Simplifying c = -2.274754878

Solution

The solution to the problem is based on the solutions from the subproblems. c = {0.274754878, -2.274754878}

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