6c^2-11c-27=

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Solution for 6c^2-11c-27= equation:


Simplifying
6c2 + -11c + -27 = 0

Reorder the terms:
-27 + -11c + 6c2 = 0

Solving
-27 + -11c + 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'.
-4.5 + -1.833333333c + c2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -1.833333333c + 4.5 + c2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -1.833333333c + c2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -1.833333333c + c2 = 0 + 4.5
-1.833333333c + c2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-1.833333333c + c2 = 4.5

The c term is -1.833333333c.  Take half its coefficient (-0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
-1.833333333c + 0.8402777775 + c2 = 4.5 + 0.8402777775

Reorder the terms:
0.8402777775 + -1.833333333c + c2 = 4.5 + 0.8402777775

Combine like terms: 4.5 + 0.8402777775 = 5.3402777775
0.8402777775 + -1.833333333c + c2 = 5.3402777775

Factor a perfect square on the left side:
(c + -0.9166666665)(c + -0.9166666665) = 5.3402777775

Calculate the square root of the right side: 2.310904104

Break this problem into two subproblems by setting 
(c + -0.9166666665) equal to 2.310904104 and -2.310904104.

Subproblem 1

c + -0.9166666665 = 2.310904104 Simplifying c + -0.9166666665 = 2.310904104 Reorder the terms: -0.9166666665 + c = 2.310904104 Solving -0.9166666665 + c = 2.310904104 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + c = 2.310904104 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + c = 2.310904104 + 0.9166666665 c = 2.310904104 + 0.9166666665 Combine like terms: 2.310904104 + 0.9166666665 = 3.2275707705 c = 3.2275707705 Simplifying c = 3.2275707705

Subproblem 2

c + -0.9166666665 = -2.310904104 Simplifying c + -0.9166666665 = -2.310904104 Reorder the terms: -0.9166666665 + c = -2.310904104 Solving -0.9166666665 + c = -2.310904104 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + c = -2.310904104 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + c = -2.310904104 + 0.9166666665 c = -2.310904104 + 0.9166666665 Combine like terms: -2.310904104 + 0.9166666665 = -1.3942374375 c = -1.3942374375 Simplifying c = -1.3942374375

Solution

The solution to the problem is based on the solutions from the subproblems. c = {3.2275707705, -1.3942374375}

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