5(k-4-2k)k-4=1

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Solution for 5(k-4-2k)k-4=1 equation: 


Simplifying
5(k + -4 + -2k) * k + -4 = 1

Reorder the terms:
5(-4 + k + -2k) * k + -4 = 1

Combine like terms: k + -2k = -1k
5(-4 + -1k) * k + -4 = 1

Reorder the terms for easier multiplication:
5k(-4 + -1k) + -4 = 1
(-4 * 5k + -1k * 5k) + -4 = 1
(-20k + -5k2) + -4 = 1

Reorder the terms:
-4 + -20k + -5k2 = 1

Solving
-4 + -20k + -5k2 = 1

Solving for variable 'k'.

Reorder the terms:
-4 + -1 + -20k + -5k2 = 1 + -1

Combine like terms: -4 + -1 = -5
-5 + -20k + -5k2 = 1 + -1

Combine like terms: 1 + -1 = 0
-5 + -20k + -5k2 = 0

Factor out the Greatest Common Factor (GCF), '-5'.
-5(1 + 4k + k2) = 0

Ignore the factor -5.

Subproblem 1
Set the factor '(1 + 4k + k2)' equal to zero and attempt to solve:

Simplifying
1 + 4k + k2 = 0

Solving
1 + 4k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 4k + -1 + k2 = 0 + -1

Reorder the terms:
1 + -1 + 4k + k2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4k + k2 = 0 + -1
4k + k2 = 0 + -1

Combine like terms: 0 + -1 = -1
4k + k2 = -1

The k term is 4k.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4k + 4 + k2 = -1 + 4

Reorder the terms:
4 + 4k + k2 = -1 + 4

Combine like terms: -1 + 4 = 3
4 + 4k + k2 = 3

Factor a perfect square on the left side:
(k + 2)(k + 2) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(k + 2) equal to 1.732050808 and -1.732050808.


Subproblem 1
k + 2 = 1.732050808

Simplifying
k + 2 = 1.732050808

Reorder the terms:
2 + k = 1.732050808

Solving
2 + k = 1.732050808

Solving for variable 'k'.

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

Add '-2' to each side of the equation.
2 + -2 + k = 1.732050808 + -2

Combine like terms: 2 + -2 = 0
0 + k = 1.732050808 + -2
k = 1.732050808 + -2

Combine like terms: 1.732050808 + -2 = -0.267949192
k = -0.267949192

Simplifying
k = -0.267949192


Subproblem 2
k + 2 = -1.732050808

Simplifying
k + 2 = -1.732050808

Reorder the terms:
2 + k = -1.732050808

Solving
2 + k = -1.732050808

Solving for variable 'k'.

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

Add '-2' to each side of the equation.
2 + -2 + k = -1.732050808 + -2

Combine like terms: 2 + -2 = 0
0 + k = -1.732050808 + -2
k = -1.732050808 + -2

Combine like terms: -1.732050808 + -2 = -3.732050808
k = -3.732050808

Simplifying
k = -3.732050808


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-0.267949192, -3.732050808}
Solution
k = {-0.267949192, -3.732050808}

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