K^2-4K-8=0I

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Solution for K^2-4K-8=0I equation: 


Simplifying
K2 + -4K + -8 = 0I

Reorder the terms:
-8 + -4K + K2 = 0I

Anything times zero is zero.
-8 + -4K + K2 = 0I

Solving
-8 + -4K + K2 = 0

Solving for variable 'K'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -4K + 8 + K2 = 0 + 8

Reorder the terms:
-8 + 8 + -4K + K2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -4K + K2 = 0 + 8
-4K + K2 = 0 + 8

Combine like terms: 0 + 8 = 8
-4K + K2 = 8

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 = 8 + 4

Reorder the terms:
4 + -4K + K2 = 8 + 4

Combine like terms: 8 + 4 = 12
4 + -4K + K2 = 12

Factor a perfect square on the left side:
(K + -2)(K + -2) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(K + -2) equal to 3.464101615 and -3.464101615.


Subproblem 1
K + -2 = 3.464101615

Simplifying
K + -2 = 3.464101615

Reorder the terms:
-2 + K = 3.464101615

Solving
-2 + K = 3.464101615

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 = 3.464101615 + 2

Combine like terms: -2 + 2 = 0
0 + K = 3.464101615 + 2
K = 3.464101615 + 2

Combine like terms: 3.464101615 + 2 = 5.464101615
K = 5.464101615

Simplifying
K = 5.464101615


Subproblem 2
K + -2 = -3.464101615

Simplifying
K + -2 = -3.464101615

Reorder the terms:
-2 + K = -3.464101615

Solving
-2 + K = -3.464101615

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 = -3.464101615 + 2

Combine like terms: -2 + 2 = 0
0 + K = -3.464101615 + 2
K = -3.464101615 + 2

Combine like terms: -3.464101615 + 2 = -1.464101615
K = -1.464101615

Simplifying
K = -1.464101615


Solution
The solution to the problem is based on the solutions
from the subproblems.
K = {5.464101615, -1.464101615}

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