3(c+8)c=7

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Solution for 3(c+8)c=7 equation:


Simplifying
3(c + 8) * c = 7

Reorder the terms:
3(8 + c) * c = 7

Reorder the terms for easier multiplication:
3c(8 + c) = 7
(8 * 3c + c * 3c) = 7
(24c + 3c2) = 7

Solving
24c + 3c2 = 7

Solving for variable 'c'.

Reorder the terms:
-7 + 24c + 3c2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 24c + 3c2 = 0

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

Divide each side by '3'.
-2.333333333 + 8c + c2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + 8c + 2.333333333 + c2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + 8c + c2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + 8c + c2 = 0 + 2.333333333
8c + c2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
8c + c2 = 2.333333333

The c term is 8c.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8c + 16 + c2 = 2.333333333 + 16

Reorder the terms:
16 + 8c + c2 = 2.333333333 + 16

Combine like terms: 2.333333333 + 16 = 18.333333333
16 + 8c + c2 = 18.333333333

Factor a perfect square on the left side:
(c + 4)(c + 4) = 18.333333333

Calculate the square root of the right side: 4.281744193

Break this problem into two subproblems by setting 
(c + 4) equal to 4.281744193 and -4.281744193.

Subproblem 1

c + 4 = 4.281744193 Simplifying c + 4 = 4.281744193 Reorder the terms: 4 + c = 4.281744193 Solving 4 + c = 4.281744193 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + c = 4.281744193 + -4 Combine like terms: 4 + -4 = 0 0 + c = 4.281744193 + -4 c = 4.281744193 + -4 Combine like terms: 4.281744193 + -4 = 0.281744193 c = 0.281744193 Simplifying c = 0.281744193

Subproblem 2

c + 4 = -4.281744193 Simplifying c + 4 = -4.281744193 Reorder the terms: 4 + c = -4.281744193 Solving 4 + c = -4.281744193 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + c = -4.281744193 + -4 Combine like terms: 4 + -4 = 0 0 + c = -4.281744193 + -4 c = -4.281744193 + -4 Combine like terms: -4.281744193 + -4 = -8.281744193 c = -8.281744193 Simplifying c = -8.281744193

Solution

The solution to the problem is based on the solutions from the subproblems. c = {0.281744193, -8.281744193}

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