4k^2+56k-14=0

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Solution for 4k^2+56k-14=0 equation: 


Simplifying
4k2 + 56k + -14 = 0

Reorder the terms:
-14 + 56k + 4k2 = 0

Solving
-14 + 56k + 4k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 28k + 2k2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + 28k + 2k2)' equal to zero and attempt to solve:

Simplifying
-7 + 28k + 2k2 = 0

Solving
-7 + 28k + 2k2 = 0

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

Divide each side by '2'.
-3.5 + 14k + k2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 14k + 3.5 + k2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 14k + k2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 14k + k2 = 0 + 3.5
14k + k2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
14k + k2 = 3.5

The k term is 14k.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14k + 49 + k2 = 3.5 + 49

Reorder the terms:
49 + 14k + k2 = 3.5 + 49

Combine like terms: 3.5 + 49 = 52.5
49 + 14k + k2 = 52.5

Factor a perfect square on the left side:
(k + 7)(k + 7) = 52.5

Calculate the square root of the right side: 7.245688373

Break this problem into two subproblems by setting 
(k + 7) equal to 7.245688373 and -7.245688373.


Subproblem 1
k + 7 = 7.245688373

Simplifying
k + 7 = 7.245688373

Reorder the terms:
7 + k = 7.245688373

Solving
7 + k = 7.245688373

Solving for variable 'k'.

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

Add '-7' to each side of the equation.
7 + -7 + k = 7.245688373 + -7

Combine like terms: 7 + -7 = 0
0 + k = 7.245688373 + -7
k = 7.245688373 + -7

Combine like terms: 7.245688373 + -7 = 0.245688373
k = 0.245688373

Simplifying
k = 0.245688373


Subproblem 2
k + 7 = -7.245688373

Simplifying
k + 7 = -7.245688373

Reorder the terms:
7 + k = -7.245688373

Solving
7 + k = -7.245688373

Solving for variable 'k'.

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

Add '-7' to each side of the equation.
7 + -7 + k = -7.245688373 + -7

Combine like terms: 7 + -7 = 0
0 + k = -7.245688373 + -7
k = -7.245688373 + -7

Combine like terms: -7.245688373 + -7 = -14.245688373
k = -14.245688373

Simplifying
k = -14.245688373


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.245688373, -14.245688373}
Solution
k = {0.245688373, -14.245688373}

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