0.4k^2+0.2k-2=0

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Solution for 0.4k^2+0.2k-2=0 equation: 


Simplifying
0.4k2 + 0.2k + -2 = 0

Reorder the terms:
-2 + 0.2k + 0.4k2 = 0

Solving
-2 + 0.2k + 0.4k2 = 0

Solving for variable 'k'.

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

Divide each side by '0.4'.
-5 + 0.5k + k2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 0.5k + 5 + k2 = 0 + 5

Reorder the terms:
-5 + 5 + 0.5k + k2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 0.5k + k2 = 0 + 5
0.5k + k2 = 0 + 5

Combine like terms: 0 + 5 = 5
0.5k + k2 = 5

The k term is 0.5k.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5k + 0.0625 + k2 = 5 + 0.0625

Reorder the terms:
0.0625 + 0.5k + k2 = 5 + 0.0625

Combine like terms: 5 + 0.0625 = 5.0625
0.0625 + 0.5k + k2 = 5.0625

Factor a perfect square on the left side:
(k + 0.25)(k + 0.25) = 5.0625

Calculate the square root of the right side: 2.25

Break this problem into two subproblems by setting 
(k + 0.25) equal to 2.25 and -2.25.


Subproblem 1
k + 0.25 = 2.25

Simplifying
k + 0.25 = 2.25

Reorder the terms:
0.25 + k = 2.25

Solving
0.25 + k = 2.25

Solving for variable 'k'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + k = 2.25 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + k = 2.25 + -0.25
k = 2.25 + -0.25

Combine like terms: 2.25 + -0.25 = 2
k = 2

Simplifying
k = 2


Subproblem 2
k + 0.25 = -2.25

Simplifying
k + 0.25 = -2.25

Reorder the terms:
0.25 + k = -2.25

Solving
0.25 + k = -2.25

Solving for variable 'k'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + k = -2.25 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + k = -2.25 + -0.25
k = -2.25 + -0.25

Combine like terms: -2.25 + -0.25 = -2.5
k = -2.5

Simplifying
k = -2.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {2, -2.5}

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