10k^2+10k=1

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

Simplifying
10k2 + 10k = 1

Reorder the terms:
10k + 10k2 = 1

Solving
10k + 10k2 = 1

Solving for variable 'k'.

Reorder the terms:
-1 + 10k + 10k2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 10k + 10k2 = 0

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

Divide each side by '10'.
-0.1 + k + k2 = 0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + k + 0.1 + k2 = 0 + 0.1

Reorder the terms:
-0.1 + 0.1 + k + k2 = 0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + k + k2 = 0 + 0.1
k + k2 = 0 + 0.1

Combine like terms: 0 + 0.1 = 0.1
k + k2 = 0.1

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 = 0.1 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + k2 = 0.1 + 0.25

Combine like terms: 0.1 + 0.25 = 0.35
1.25 + k2 = 0.35

Factor a perfect square on the left side:
(k + 0.5)(k + 0.5) = 0.35

Calculate the square root of the right side: 0.591607978

Break this problem into two subproblems by setting 
(k + 0.5) equal to 0.591607978 and -0.591607978.

Subproblem 1
k + 0.5 = 0.591607978

Simplifying
k + 0.5 = 0.591607978

Reorder the terms:
0.5 + k = 0.591607978

Solving
0.5 + k = 0.591607978

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 = 0.591607978 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + k = 0.591607978 + -0.5
k = 0.591607978 + -0.5

Combine like terms: 0.591607978 + -0.5 = 0.091607978
k = 0.091607978

Simplifying
k = 0.091607978

Subproblem 2
k + 0.5 = -0.591607978

Simplifying
k + 0.5 = -0.591607978

Reorder the terms:
0.5 + k = -0.591607978

Solving
0.5 + k = -0.591607978

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 = -0.591607978 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + k = -0.591607978 + -0.5
k = -0.591607978 + -0.5

Combine like terms: -0.591607978 + -0.5 = -1.091607978
k = -1.091607978

Simplifying
k = -1.091607978

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.091607978, -1.091607978}