k^2-k=-0.25

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Solution for k^2-k=-0.25 equation: 


Simplifying
k2 + -1k = -0.25

Reorder the terms:
-1k + k2 = -0.25

Solving
-1k + k2 = -0.25

Solving for variable 'k'.

Reorder the terms:
0.25 + -1k + k2 = -0.25 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.25 + -1k + k2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -1k + -0.25 + k2 = 0.00 + -0.25

Reorder the terms:
0.25 + -0.25 + -1k + k2 = 0.00 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -1k + k2 = 0.00 + -0.25
-1k + k2 = 0.00 + -0.25

Combine like terms: 0.00 + -0.25 = -0.25
-1k + k2 = -0.25

The k term is -1k.  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.
-1k + 0.25 + k2 = -0.25 + 0.25

Reorder the terms:
0.25 + -1k + k2 = -0.25 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.25 + -1k + k2 = 0.00

Factor a perfect square on the left side:
(k + -0.5)(k + -0.5) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(k + -0.5) equal to 0.00 and 0.00.


Subproblem 1
k + -0.5 = 0.00

Simplifying
k + -0.5 = 0.00

Reorder the terms:
-0.5 + k = 0.00

Solving
-0.5 + k = 0.00

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 = 0.00 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + k = 0.00 + 0.5
k = 0.00 + 0.5

Combine like terms: 0.00 + 0.5 = 0.5
k = 0.5

Simplifying
k = 0.5


Subproblem 2
k + -0.5 = 0.00

Simplifying
k + -0.5 = 0.00

Reorder the terms:
-0.5 + k = 0.00

Solving
-0.5 + k = 0.00

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 = 0.00 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + k = 0.00 + 0.5
k = 0.00 + 0.5

Combine like terms: 0.00 + 0.5 = 0.5
k = 0.5

Simplifying
k = 0.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.5, 0.5}

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