2k^2=10k+2

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 = 5.192582404
k = 5.192582404

Simplifying
k = 5.192582404

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 = -0.192582404
k = -0.192582404

Simplifying
k = -0.192582404

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