144-4k^2+16-4k+16=0

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Solution for 144-4k^2+16-4k+16=0 equation: 


Simplifying
144 + -4k2 + 16 + -4k + 16 = 0

Reorder the terms:
144 + 16 + 16 + -4k + -4k2 = 0

Combine like terms: 144 + 16 = 160
160 + 16 + -4k + -4k2 = 0

Combine like terms: 160 + 16 = 176
176 + -4k + -4k2 = 0

Solving
176 + -4k + -4k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '4'.
4(44 + -1k + -1k2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(44 + -1k + -1k2)' equal to zero and attempt to solve:

Simplifying
44 + -1k + -1k2 = 0

Solving
44 + -1k + -1k2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-44 + k + k2 = 0

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + k + 44 + k2 = 0 + 44

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

Combine like terms: -44 + 44 = 0
0 + k + k2 = 0 + 44
k + k2 = 0 + 44

Combine like terms: 0 + 44 = 44
k + k2 = 44

The k term is k.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + k2 = 44 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + k2 = 44 + 0.25

Combine like terms: 44 + 0.25 = 44.25
1.25 + k2 = 44.25

Factor a perfect square on the left side:
(k + 0.5)(k + 0.5) = 44.25

Calculate the square root of the right side: 6.652067348

Break this problem into two subproblems by setting 
(k + 0.5) equal to 6.652067348 and -6.652067348.


Subproblem 1
k + 0.5 = 6.652067348

Simplifying
k + 0.5 = 6.652067348

Reorder the terms:
0.5 + k = 6.652067348

Solving
0.5 + k = 6.652067348

Solving for variable 'k'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + k = 6.652067348 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + k = 6.652067348 + -0.5
k = 6.652067348 + -0.5

Combine like terms: 6.652067348 + -0.5 = 6.152067348
k = 6.152067348

Simplifying
k = 6.152067348


Subproblem 2
k + 0.5 = -6.652067348

Simplifying
k + 0.5 = -6.652067348

Reorder the terms:
0.5 + k = -6.652067348

Solving
0.5 + k = -6.652067348

Solving for variable 'k'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + k = -6.652067348 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + k = -6.652067348 + -0.5
k = -6.652067348 + -0.5

Combine like terms: -6.652067348 + -0.5 = -7.152067348
k = -7.152067348

Simplifying
k = -7.152067348


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {6.152067348, -7.152067348}
Solution
k = {6.152067348, -7.152067348}

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