10k^2-20k+12=3

Solution for 10k^2-20k+12=3 equation:

Simplifying
10k2 + -20k + 12 = 3

Reorder the terms:
12 + -20k + 10k2 = 3

Solving
12 + -20k + 10k2 = 3

Solving for variable 'k'.

Reorder the terms:
12 + -3 + -20k + 10k2 = 3 + -3

Combine like terms: 12 + -3 = 9
9 + -20k + 10k2 = 3 + -3

Combine like terms: 3 + -3 = 0
9 + -20k + 10k2 = 0

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

Divide each side by '10'.
0.9 + -2k + k2 = 0

Move the constant term to the right:

Add '-0.9' to each side of the equation.
0.9 + -2k + -0.9 + k2 = 0 + -0.9

Reorder the terms:
0.9 + -0.9 + -2k + k2 = 0 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + -2k + k2 = 0 + -0.9
-2k + k2 = 0 + -0.9

Combine like terms: 0 + -0.9 = -0.9
-2k + k2 = -0.9

The k term is -2k.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2k + 1 + k2 = -0.9 + 1

Reorder the terms:
1 + -2k + k2 = -0.9 + 1

Combine like terms: -0.9 + 1 = 0.1
1 + -2k + k2 = 0.1

Factor a perfect square on the left side:
(k + -1)(k + -1) = 0.1

Calculate the square root of the right side: 0.316227766

Break this problem into two subproblems by setting 
(k + -1) equal to 0.316227766 and -0.316227766.

Subproblem 1
k + -1 = 0.316227766

Simplifying
k + -1 = 0.316227766

Reorder the terms:
-1 + k = 0.316227766

Solving
-1 + k = 0.316227766

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 1 + k = 0.316227766 + 1

Combine like terms: -1 + 1 = 0
0 + k = 0.316227766 + 1
k = 0.316227766 + 1

Combine like terms: 0.316227766 + 1 = 1.316227766
k = 1.316227766

Simplifying
k = 1.316227766

Subproblem 2
k + -1 = -0.316227766

Simplifying
k + -1 = -0.316227766

Reorder the terms:
-1 + k = -0.316227766

Solving
-1 + k = -0.316227766

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 1 + k = -0.316227766 + 1

Combine like terms: -1 + 1 = 0
0 + k = -0.316227766 + 1
k = -0.316227766 + 1

Combine like terms: -0.316227766 + 1 = 0.683772234
k = 0.683772234

Simplifying
k = 0.683772234

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.316227766, 0.683772234}