3k^2+11k-10=0

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Solution for 3k^2+11k-10=0 equation: 


Simplifying
3k2 + 11k + -10 = 0

Reorder the terms:
-10 + 11k + 3k2 = 0

Solving
-10 + 11k + 3k2 = 0

Solving for variable 'k'.

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

Divide each side by '3'.
-3.333333333 + 3.666666667k + k2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 3.666666667k + 3.333333333 + k2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 3.666666667k + k2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 3.666666667k + k2 = 0 + 3.333333333
3.666666667k + k2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
3.666666667k + k2 = 3.333333333

The k term is 3.666666667k.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667k + 3.361111114 + k2 = 3.333333333 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667k + k2 = 3.333333333 + 3.361111114

Combine like terms: 3.333333333 + 3.361111114 = 6.694444447
3.361111114 + 3.666666667k + k2 = 6.694444447

Factor a perfect square on the left side:
(k + 1.833333334)(k + 1.833333334) = 6.694444447

Calculate the square root of the right side: 2.58736245

Break this problem into two subproblems by setting 
(k + 1.833333334) equal to 2.58736245 and -2.58736245.


Subproblem 1
k + 1.833333334 = 2.58736245

Simplifying
k + 1.833333334 = 2.58736245

Reorder the terms:
1.833333334 + k = 2.58736245

Solving
1.833333334 + k = 2.58736245

Solving for variable 'k'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + k = 2.58736245 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + k = 2.58736245 + -1.833333334
k = 2.58736245 + -1.833333334

Combine like terms: 2.58736245 + -1.833333334 = 0.754029116
k = 0.754029116

Simplifying
k = 0.754029116


Subproblem 2
k + 1.833333334 = -2.58736245

Simplifying
k + 1.833333334 = -2.58736245

Reorder the terms:
1.833333334 + k = -2.58736245

Solving
1.833333334 + k = -2.58736245

Solving for variable 'k'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + k = -2.58736245 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + k = -2.58736245 + -1.833333334
k = -2.58736245 + -1.833333334

Combine like terms: -2.58736245 + -1.833333334 = -4.420695784
k = -4.420695784

Simplifying
k = -4.420695784


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.754029116, -4.420695784}

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