3c^2-3c-5=0

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Solution for 3c^2-3c-5=0 equation:


Simplifying
3c2 + -3c + -5 = 0

Reorder the terms:
-5 + -3c + 3c2 = 0

Solving
-5 + -3c + 3c2 = 0

Solving for variable 'c'.

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

Divide each side by '3'.
-1.666666667 + -1c + c2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -1c + 1.666666667 + c2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -1c + c2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -1c + c2 = 0 + 1.666666667
-1c + c2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-1c + c2 = 1.666666667

The c term is -1c.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1c + 0.25 + c2 = 1.666666667 + 0.25

Reorder the terms:
0.25 + -1c + c2 = 1.666666667 + 0.25

Combine like terms: 1.666666667 + 0.25 = 1.916666667
0.25 + -1c + c2 = 1.916666667

Factor a perfect square on the left side:
(c + -0.5)(c + -0.5) = 1.916666667

Calculate the square root of the right side: 1.384437311

Break this problem into two subproblems by setting 
(c + -0.5) equal to 1.384437311 and -1.384437311.

Subproblem 1

c + -0.5 = 1.384437311 Simplifying c + -0.5 = 1.384437311 Reorder the terms: -0.5 + c = 1.384437311 Solving -0.5 + c = 1.384437311 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + c = 1.384437311 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + c = 1.384437311 + 0.5 c = 1.384437311 + 0.5 Combine like terms: 1.384437311 + 0.5 = 1.884437311 c = 1.884437311 Simplifying c = 1.884437311

Subproblem 2

c + -0.5 = -1.384437311 Simplifying c + -0.5 = -1.384437311 Reorder the terms: -0.5 + c = -1.384437311 Solving -0.5 + c = -1.384437311 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + c = -1.384437311 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + c = -1.384437311 + 0.5 c = -1.384437311 + 0.5 Combine like terms: -1.384437311 + 0.5 = -0.884437311 c = -0.884437311 Simplifying c = -0.884437311

Solution

The solution to the problem is based on the solutions from the subproblems. c = {1.884437311, -0.884437311}

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