5k^2+10k+1=0

Solution for 5k^2+10k+1=0 equation:

Simplifying
5k2 + 10k + 1 = 0

Reorder the terms:
1 + 10k + 5k2 = 0

Solving
1 + 10k + 5k2 = 0

Solving for variable 'k'.

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

Divide each side by '5'.
0.2 + 2k + k2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 2k + -0.2 + k2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 2k + k2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 2k + k2 = 0 + -0.2
2k + k2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
2k + k2 = -0.2

The k term is 2k.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2k + 1 + k2 = -0.2 + 1

Reorder the terms:
1 + 2k + k2 = -0.2 + 1

Combine like terms: -0.2 + 1 = 0.8
1 + 2k + k2 = 0.8

Factor a perfect square on the left side:
(k + 1)(k + 1) = 0.8

Calculate the square root of the right side: 0.894427191

Break this problem into two subproblems by setting 
(k + 1) equal to 0.894427191 and -0.894427191.

Subproblem 1
k + 1 = 0.894427191

Simplifying
k + 1 = 0.894427191

Reorder the terms:
1 + k = 0.894427191

Solving
1 + k = 0.894427191

Solving for variable 'k'.

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

Add '-1' to each side of the equation.
1 + -1 + k = 0.894427191 + -1

Combine like terms: 1 + -1 = 0
0 + k = 0.894427191 + -1
k = 0.894427191 + -1

Combine like terms: 0.894427191 + -1 = -0.105572809
k = -0.105572809

Simplifying
k = -0.105572809

Subproblem 2
k + 1 = -0.894427191

Simplifying
k + 1 = -0.894427191

Reorder the terms:
1 + k = -0.894427191

Solving
1 + k = -0.894427191

Solving for variable 'k'.

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

Add '-1' to each side of the equation.
1 + -1 + k = -0.894427191 + -1

Combine like terms: 1 + -1 = 0
0 + k = -0.894427191 + -1
k = -0.894427191 + -1

Combine like terms: -0.894427191 + -1 = -1.894427191
k = -1.894427191

Simplifying
k = -1.894427191

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-0.105572809, -1.894427191}