6k^2+6k-5=0

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Solution for 6k^2+6k-5=0 equation:


Simplifying
6k2 + 6k + -5 = 0

Reorder the terms:
-5 + 6k + 6k2 = 0

Solving
-5 + 6k + 6k2 = 0

Solving for variable 'k'.

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

Divide each side by '6'.
-0.8333333333 + k + k2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + k + 0.8333333333 + k2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + k + k2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + k + k2 = 0 + 0.8333333333
k + k2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
k + k2 = 0.8333333333

The k term is k.  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.
 + 0.25 + k2 = 0.8333333333 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + k2 = 0.8333333333 + 0.25

Combine like terms: 0.8333333333 + 0.25 = 1.0833333333
1.25 + k2 = 1.0833333333

Factor a perfect square on the left side:
(k + 0.5)(k + 0.5) = 1.0833333333

Calculate the square root of the right side: 1.040833

Break this problem into two subproblems by setting 
(k + 0.5) equal to 1.040833 and -1.040833.

Subproblem 1

k + 0.5 = 1.040833 Simplifying k + 0.5 = 1.040833 Reorder the terms: 0.5 + k = 1.040833 Solving 0.5 + k = 1.040833 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + k = 1.040833 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + k = 1.040833 + -0.5 k = 1.040833 + -0.5 Combine like terms: 1.040833 + -0.5 = 0.540833 k = 0.540833 Simplifying k = 0.540833

Subproblem 2

k + 0.5 = -1.040833 Simplifying k + 0.5 = -1.040833 Reorder the terms: 0.5 + k = -1.040833 Solving 0.5 + k = -1.040833 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + k = -1.040833 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + k = -1.040833 + -0.5 k = -1.040833 + -0.5 Combine like terms: -1.040833 + -0.5 = -1.540833 k = -1.540833 Simplifying k = -1.540833

Solution

The solution to the problem is based on the solutions from the subproblems. k = {0.540833, -1.540833}

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