2k^2+18k+2=0

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Solution for 2k^2+18k+2=0 equation: 


Simplifying
2k2 + 18k + 2 = 0

Reorder the terms:
2 + 18k + 2k2 = 0

Solving
2 + 18k + 2k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 9k + k2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + 9k + k2)' equal to zero and attempt to solve:

Simplifying
1 + 9k + k2 = 0

Solving
1 + 9k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 9k + -1 + k2 = 0 + -1

Reorder the terms:
1 + -1 + 9k + k2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 9k + k2 = 0 + -1
9k + k2 = 0 + -1

Combine like terms: 0 + -1 = -1
9k + k2 = -1

The k term is 9k.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9k + 20.25 + k2 = -1 + 20.25

Reorder the terms:
20.25 + 9k + k2 = -1 + 20.25

Combine like terms: -1 + 20.25 = 19.25
20.25 + 9k + k2 = 19.25

Factor a perfect square on the left side:
(k + 4.5)(k + 4.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(k + 4.5) equal to 4.387482194 and -4.387482194.


Subproblem 1
k + 4.5 = 4.387482194

Simplifying
k + 4.5 = 4.387482194

Reorder the terms:
4.5 + k = 4.387482194

Solving
4.5 + k = 4.387482194

Solving for variable 'k'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + k = 4.387482194 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + k = 4.387482194 + -4.5
k = 4.387482194 + -4.5

Combine like terms: 4.387482194 + -4.5 = -0.112517806
k = -0.112517806

Simplifying
k = -0.112517806


Subproblem 2
k + 4.5 = -4.387482194

Simplifying
k + 4.5 = -4.387482194

Reorder the terms:
4.5 + k = -4.387482194

Solving
4.5 + k = -4.387482194

Solving for variable 'k'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + k = -4.387482194 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + k = -4.387482194 + -4.5
k = -4.387482194 + -4.5

Combine like terms: -4.387482194 + -4.5 = -8.887482194
k = -8.887482194

Simplifying
k = -8.887482194


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-0.112517806, -8.887482194}
Solution
k = {-0.112517806, -8.887482194}

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