4k^2-20k-44=0

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Solution for 4k^2-20k-44=0 equation: 


Simplifying
4k2 + -20k + -44 = 0

Reorder the terms:
-44 + -20k + 4k2 = 0

Solving
-44 + -20k + 4k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-11 + -5k + k2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-11 + -5k + k2)' equal to zero and attempt to solve:

Simplifying
-11 + -5k + k2 = 0

Solving
-11 + -5k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -5k + 11 + k2 = 0 + 11

Reorder the terms:
-11 + 11 + -5k + k2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -5k + k2 = 0 + 11
-5k + k2 = 0 + 11

Combine like terms: 0 + 11 = 11
-5k + k2 = 11

The k term is -5k.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5k + 6.25 + k2 = 11 + 6.25

Reorder the terms:
6.25 + -5k + k2 = 11 + 6.25

Combine like terms: 11 + 6.25 = 17.25
6.25 + -5k + k2 = 17.25

Factor a perfect square on the left side:
(k + -2.5)(k + -2.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(k + -2.5) equal to 4.153311931 and -4.153311931.


Subproblem 1
k + -2.5 = 4.153311931

Simplifying
k + -2.5 = 4.153311931

Reorder the terms:
-2.5 + k = 4.153311931

Solving
-2.5 + k = 4.153311931

Solving for variable 'k'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + k = 4.153311931 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + k = 4.153311931 + 2.5
k = 4.153311931 + 2.5

Combine like terms: 4.153311931 + 2.5 = 6.653311931
k = 6.653311931

Simplifying
k = 6.653311931


Subproblem 2
k + -2.5 = -4.153311931

Simplifying
k + -2.5 = -4.153311931

Reorder the terms:
-2.5 + k = -4.153311931

Solving
-2.5 + k = -4.153311931

Solving for variable 'k'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + k = -4.153311931 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + k = -4.153311931 + 2.5
k = -4.153311931 + 2.5

Combine like terms: -4.153311931 + 2.5 = -1.653311931
k = -1.653311931

Simplifying
k = -1.653311931


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {6.653311931, -1.653311931}
Solution
k = {6.653311931, -1.653311931}

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