3k^2-6k-43=-2

Solution for 3k^2-6k-43=-2 equation:

Simplifying
3k2 + -6k + -43 = -2

Reorder the terms:
-43 + -6k + 3k2 = -2

Solving
-43 + -6k + 3k2 = -2

Solving for variable 'k'.

Reorder the terms:
-43 + 2 + -6k + 3k2 = -2 + 2

Combine like terms: -43 + 2 = -41
-41 + -6k + 3k2 = -2 + 2

Combine like terms: -2 + 2 = 0
-41 + -6k + 3k2 = 0

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

Divide each side by '3'.
-13.66666667 + -2k + k2 = 0

Move the constant term to the right:

Add '13.66666667' to each side of the equation.
-13.66666667 + -2k + 13.66666667 + k2 = 0 + 13.66666667

Reorder the terms:
-13.66666667 + 13.66666667 + -2k + k2 = 0 + 13.66666667

Combine like terms: -13.66666667 + 13.66666667 = 0.00000000
0.00000000 + -2k + k2 = 0 + 13.66666667
-2k + k2 = 0 + 13.66666667

Combine like terms: 0 + 13.66666667 = 13.66666667
-2k + k2 = 13.66666667

The k term is -2k.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2k + 1 + k2 = 13.66666667 + 1

Reorder the terms:
1 + -2k + k2 = 13.66666667 + 1

Combine like terms: 13.66666667 + 1 = 14.66666667
1 + -2k + k2 = 14.66666667

Factor a perfect square on the left side:
(k + -1)(k + -1) = 14.66666667

Calculate the square root of the right side: 3.829708431

Break this problem into two subproblems by setting 
(k + -1) equal to 3.829708431 and -3.829708431.

Subproblem 1
k + -1 = 3.829708431

Simplifying
k + -1 = 3.829708431

Reorder the terms:
-1 + k = 3.829708431

Solving
-1 + k = 3.829708431

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 1 + k = 3.829708431 + 1

Combine like terms: -1 + 1 = 0
0 + k = 3.829708431 + 1
k = 3.829708431 + 1

Combine like terms: 3.829708431 + 1 = 4.829708431
k = 4.829708431

Simplifying
k = 4.829708431

Subproblem 2
k + -1 = -3.829708431

Simplifying
k + -1 = -3.829708431

Reorder the terms:
-1 + k = -3.829708431

Solving
-1 + k = -3.829708431

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 1 + k = -3.829708431 + 1

Combine like terms: -1 + 1 = 0
0 + k = -3.829708431 + 1
k = -3.829708431 + 1

Combine like terms: -3.829708431 + 1 = -2.829708431
k = -2.829708431

Simplifying
k = -2.829708431

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {4.829708431, -2.829708431}