c^2-6c-4.67=2.5

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Solution for c^2-6c-4.67=2.5 equation:


Simplifying
c2 + -6c + -4.67 = 2.5

Reorder the terms:
-4.67 + -6c + c2 = 2.5

Solving
-4.67 + -6c + c2 = 2.5

Solving for variable 'c'.

Reorder the terms:
-4.67 + -2.5 + -6c + c2 = 2.5 + -2.5

Combine like terms: -4.67 + -2.5 = -7.17
-7.17 + -6c + c2 = 2.5 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
-7.17 + -6c + c2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '7.17' to each side of the equation.
-7.17 + -6c + 7.17 + c2 = 0.0 + 7.17

Reorder the terms:
-7.17 + 7.17 + -6c + c2 = 0.0 + 7.17

Combine like terms: -7.17 + 7.17 = 0.00
0.00 + -6c + c2 = 0.0 + 7.17
-6c + c2 = 0.0 + 7.17

Combine like terms: 0.0 + 7.17 = 7.17
-6c + c2 = 7.17

The c term is -6c.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6c + 9 + c2 = 7.17 + 9

Reorder the terms:
9 + -6c + c2 = 7.17 + 9

Combine like terms: 7.17 + 9 = 16.17
9 + -6c + c2 = 16.17

Factor a perfect square on the left side:
(c + -3)(c + -3) = 16.17

Calculate the square root of the right side: 4.021193853

Break this problem into two subproblems by setting 
(c + -3) equal to 4.021193853 and -4.021193853.

Subproblem 1

c + -3 = 4.021193853 Simplifying c + -3 = 4.021193853 Reorder the terms: -3 + c = 4.021193853 Solving -3 + c = 4.021193853 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + c = 4.021193853 + 3 Combine like terms: -3 + 3 = 0 0 + c = 4.021193853 + 3 c = 4.021193853 + 3 Combine like terms: 4.021193853 + 3 = 7.021193853 c = 7.021193853 Simplifying c = 7.021193853

Subproblem 2

c + -3 = -4.021193853 Simplifying c + -3 = -4.021193853 Reorder the terms: -3 + c = -4.021193853 Solving -3 + c = -4.021193853 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + c = -4.021193853 + 3 Combine like terms: -3 + 3 = 0 0 + c = -4.021193853 + 3 c = -4.021193853 + 3 Combine like terms: -4.021193853 + 3 = -1.021193853 c = -1.021193853 Simplifying c = -1.021193853

Solution

The solution to the problem is based on the solutions from the subproblems. c = {7.021193853, -1.021193853}

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