2k^2-2k-5=-3

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Solution for 2k^2-2k-5=-3 equation: 


Simplifying
2k2 + -2k + -5 = -3

Reorder the terms:
-5 + -2k + 2k2 = -3

Solving
-5 + -2k + 2k2 = -3

Solving for variable 'k'.

Reorder the terms:
-5 + 3 + -2k + 2k2 = -3 + 3

Combine like terms: -5 + 3 = -2
-2 + -2k + 2k2 = -3 + 3

Combine like terms: -3 + 3 = 0
-2 + -2k + 2k2 = 0

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

Ignore the factor 2.

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

Simplifying
-1 + -1k + k2 = 0

Solving
-1 + -1k + k2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 1 + 0.25

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

Combine like terms: 1 + 0.25 = 1.25
0.25 + -1k + k2 = 1.25

Factor a perfect square on the left side:
(k + -0.5)(k + -0.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(k + -0.5) equal to 1.118033989 and -1.118033989.


Subproblem 1
k + -0.5 = 1.118033989

Simplifying
k + -0.5 = 1.118033989

Reorder the terms:
-0.5 + k = 1.118033989

Solving
-0.5 + k = 1.118033989

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 = 1.118033989 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + k = 1.118033989 + 0.5
k = 1.118033989 + 0.5

Combine like terms: 1.118033989 + 0.5 = 1.618033989
k = 1.618033989

Simplifying
k = 1.618033989


Subproblem 2
k + -0.5 = -1.118033989

Simplifying
k + -0.5 = -1.118033989

Reorder the terms:
-0.5 + k = -1.118033989

Solving
-0.5 + k = -1.118033989

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 = -1.118033989 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + k = -1.118033989 + 0.5
k = -1.118033989 + 0.5

Combine like terms: -1.118033989 + 0.5 = -0.618033989
k = -0.618033989

Simplifying
k = -0.618033989


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.618033989, -0.618033989}
Solution
k = {1.618033989, -0.618033989}

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