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 = 5.25
6.25 + -5k + k2 = 5.25

Factor a perfect square on the left side:
(k + -2.5)(k + -2.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(k + -2.5) equal to 2.291287847 and -2.291287847.


Subproblem 1
k + -2.5 = 2.291287847

Simplifying
k + -2.5 = 2.291287847

Reorder the terms:
-2.5 + k = 2.291287847

Solving
-2.5 + k = 2.291287847

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 = 2.291287847 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + k = 2.291287847 + 2.5
k = 2.291287847 + 2.5

Combine like terms: 2.291287847 + 2.5 = 4.791287847
k = 4.791287847

Simplifying
k = 4.791287847


Subproblem 2
k + -2.5 = -2.291287847

Simplifying
k + -2.5 = -2.291287847

Reorder the terms:
-2.5 + k = -2.291287847

Solving
-2.5 + k = -2.291287847

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 = -2.291287847 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + k = -2.291287847 + 2.5
k = -2.291287847 + 2.5

Combine like terms: -2.291287847 + 2.5 = 0.208712153
k = 0.208712153

Simplifying
k = 0.208712153


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {4.791287847, 0.208712153}
Solution
k = {4.791287847, 0.208712153}

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