2k^2=-10k+2

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


Simplifying
2k2 = -10k + 2

Reorder the terms:
2k2 = 2 + -10k

Solving
2k2 = 2 + -10k

Solving for variable 'k'.

Reorder the terms:
-2 + 10k + 2k2 = 2 + -10k + -2 + 10k

Reorder the terms:
-2 + 10k + 2k2 = 2 + -2 + -10k + 10k

Combine like terms: 2 + -2 = 0
-2 + 10k + 2k2 = 0 + -10k + 10k
-2 + 10k + 2k2 = -10k + 10k

Combine like terms: -10k + 10k = 0
-2 + 10k + 2k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 5k + k2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + 5k + k2)' equal to zero and attempt to solve:

Simplifying
-1 + 5k + k2 = 0

Solving
-1 + 5k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 5k + 1 + k2 = 0 + 1

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

Combine like terms: -1 + 1 = 0
0 + 5k + k2 = 0 + 1
5k + k2 = 0 + 1

Combine like terms: 0 + 1 = 1
5k + k2 = 1

The k term is 5k.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5k + 6.25 + k2 = 1 + 6.25

Reorder the terms:
6.25 + 5k + k2 = 1 + 6.25

Combine like terms: 1 + 6.25 = 7.25
6.25 + 5k + k2 = 7.25

Factor a perfect square on the left side:
(k + 2.5)(k + 2.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(k + 2.5) equal to 2.692582404 and -2.692582404.


Subproblem 1
k + 2.5 = 2.692582404

Simplifying
k + 2.5 = 2.692582404

Reorder the terms:
2.5 + k = 2.692582404

Solving
2.5 + k = 2.692582404

Solving for variable 'k'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + k = 2.692582404 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + k = 2.692582404 + -2.5
k = 2.692582404 + -2.5

Combine like terms: 2.692582404 + -2.5 = 0.192582404
k = 0.192582404

Simplifying
k = 0.192582404


Subproblem 2
k + 2.5 = -2.692582404

Simplifying
k + 2.5 = -2.692582404

Reorder the terms:
2.5 + k = -2.692582404

Solving
2.5 + k = -2.692582404

Solving for variable 'k'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + k = -2.692582404 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + k = -2.692582404 + -2.5
k = -2.692582404 + -2.5

Combine like terms: -2.692582404 + -2.5 = -5.192582404
k = -5.192582404

Simplifying
k = -5.192582404


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.192582404, -5.192582404}
Solution
k = {0.192582404, -5.192582404}

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