6c^2-c-3=0

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Solution for 6c^2-c-3=0 equation: 


Simplifying
6c2 + -1c + -3 = 0

Reorder the terms:
-3 + -1c + 6c2 = 0

Solving
-3 + -1c + 6c2 = 0

Solving for variable 'c'.

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

Divide each side by '6'.
-0.5 + -0.1666666667c + c2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.1666666667c + 0.5 + c2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.1666666667c + c2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.1666666667c + c2 = 0 + 0.5
-0.1666666667c + c2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.1666666667c + c2 = 0.5

The c term is -0.1666666667c.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667c + 0.006944444447 + c2 = 0.5 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667c + c2 = 0.5 + 0.006944444447

Combine like terms: 0.5 + 0.006944444447 = 0.506944444447
0.006944444447 + -0.1666666667c + c2 = 0.506944444447

Factor a perfect square on the left side:
(c + -0.08333333335)(c + -0.08333333335) = 0.506944444447

Calculate the square root of the right side: 0.712000312

Break this problem into two subproblems by setting 
(c + -0.08333333335) equal to 0.712000312 and -0.712000312.


Subproblem 1
c + -0.08333333335 = 0.712000312

Simplifying
c + -0.08333333335 = 0.712000312

Reorder the terms:
-0.08333333335 + c = 0.712000312

Solving
-0.08333333335 + c = 0.712000312

Solving for variable 'c'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + c = 0.712000312 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + c = 0.712000312 + 0.08333333335
c = 0.712000312 + 0.08333333335

Combine like terms: 0.712000312 + 0.08333333335 = 0.79533364535
c = 0.79533364535

Simplifying
c = 0.79533364535


Subproblem 2
c + -0.08333333335 = -0.712000312

Simplifying
c + -0.08333333335 = -0.712000312

Reorder the terms:
-0.08333333335 + c = -0.712000312

Solving
-0.08333333335 + c = -0.712000312

Solving for variable 'c'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + c = -0.712000312 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + c = -0.712000312 + 0.08333333335
c = -0.712000312 + 0.08333333335

Combine like terms: -0.712000312 + 0.08333333335 = -0.62866697865
c = -0.62866697865

Simplifying
c = -0.62866697865


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.79533364535, -0.62866697865}

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