6k^2+112k+48=

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Solution for 6k^2+112k+48= equation:


Simplifying
6k2 + 112k + 48 = 0

Reorder the terms:
48 + 112k + 6k2 = 0

Solving
48 + 112k + 6k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 56k + 3k2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(24 + 56k + 3k2)' equal to zero and attempt to solve:

Simplifying
24 + 56k + 3k2 = 0

Solving
24 + 56k + 3k2 = 0

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

Divide each side by '3'.
8 + 18.66666667k + k2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 18.66666667k + -8 + k2 = 0 + -8

Reorder the terms:
8 + -8 + 18.66666667k + k2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 18.66666667k + k2 = 0 + -8
18.66666667k + k2 = 0 + -8

Combine like terms: 0 + -8 = -8
18.66666667k + k2 = -8

The k term is 18.66666667k.  Take half its coefficient (9.333333335).
Square it (87.11111114) and add it to both sides.

Add '87.11111114' to each side of the equation.
18.66666667k + 87.11111114 + k2 = -8 + 87.11111114

Reorder the terms:
87.11111114 + 18.66666667k + k2 = -8 + 87.11111114

Combine like terms: -8 + 87.11111114 = 79.11111114
87.11111114 + 18.66666667k + k2 = 79.11111114

Factor a perfect square on the left side:
(k + 9.333333335)(k + 9.333333335) = 79.11111114

Calculate the square root of the right side: 8.894442711

Break this problem into two subproblems by setting 
(k + 9.333333335) equal to 8.894442711 and -8.894442711.


Subproblem 1
k + 9.333333335 = 8.894442711

Simplifying
k + 9.333333335 = 8.894442711

Reorder the terms:
9.333333335 + k = 8.894442711

Solving
9.333333335 + k = 8.894442711

Solving for variable 'k'.

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

Add '-9.333333335' to each side of the equation.
9.333333335 + -9.333333335 + k = 8.894442711 + -9.333333335

Combine like terms: 9.333333335 + -9.333333335 = 0.000000000
0.000000000 + k = 8.894442711 + -9.333333335
k = 8.894442711 + -9.333333335

Combine like terms: 8.894442711 + -9.333333335 = -0.438890624
k = -0.438890624

Simplifying
k = -0.438890624


Subproblem 2
k + 9.333333335 = -8.894442711

Simplifying
k + 9.333333335 = -8.894442711

Reorder the terms:
9.333333335 + k = -8.894442711

Solving
9.333333335 + k = -8.894442711

Solving for variable 'k'.

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

Add '-9.333333335' to each side of the equation.
9.333333335 + -9.333333335 + k = -8.894442711 + -9.333333335

Combine like terms: 9.333333335 + -9.333333335 = 0.000000000
0.000000000 + k = -8.894442711 + -9.333333335
k = -8.894442711 + -9.333333335

Combine like terms: -8.894442711 + -9.333333335 = -18.227776046
k = -18.227776046

Simplifying
k = -18.227776046


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-0.438890624, -18.227776046}
Solution
k = {-0.438890624, -18.227776046}

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