4k^2+40k-124=0

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Solution for 4k^2+40k-124=0 equation: 


Simplifying
4k2 + 40k + -124 = 0

Reorder the terms:
-124 + 40k + 4k2 = 0

Solving
-124 + 40k + 4k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-31 + 10k + k2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-31 + 10k + k2)' equal to zero and attempt to solve:

Simplifying
-31 + 10k + k2 = 0

Solving
-31 + 10k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 10k + 31 + k2 = 0 + 31

Reorder the terms:
-31 + 31 + 10k + k2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 10k + k2 = 0 + 31
10k + k2 = 0 + 31

Combine like terms: 0 + 31 = 31
10k + k2 = 31

The k term is 10k.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10k + 25 + k2 = 31 + 25

Reorder the terms:
25 + 10k + k2 = 31 + 25

Combine like terms: 31 + 25 = 56
25 + 10k + k2 = 56

Factor a perfect square on the left side:
(k + 5)(k + 5) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(k + 5) equal to 7.483314774 and -7.483314774.


Subproblem 1
k + 5 = 7.483314774

Simplifying
k + 5 = 7.483314774

Reorder the terms:
5 + k = 7.483314774

Solving
5 + k = 7.483314774

Solving for variable 'k'.

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

Add '-5' to each side of the equation.
5 + -5 + k = 7.483314774 + -5

Combine like terms: 5 + -5 = 0
0 + k = 7.483314774 + -5
k = 7.483314774 + -5

Combine like terms: 7.483314774 + -5 = 2.483314774
k = 2.483314774

Simplifying
k = 2.483314774


Subproblem 2
k + 5 = -7.483314774

Simplifying
k + 5 = -7.483314774

Reorder the terms:
5 + k = -7.483314774

Solving
5 + k = -7.483314774

Solving for variable 'k'.

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

Add '-5' to each side of the equation.
5 + -5 + k = -7.483314774 + -5

Combine like terms: 5 + -5 = 0
0 + k = -7.483314774 + -5
k = -7.483314774 + -5

Combine like terms: -7.483314774 + -5 = -12.483314774
k = -12.483314774

Simplifying
k = -12.483314774


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {2.483314774, -12.483314774}
Solution
k = {2.483314774, -12.483314774}

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