Simplifying
50k^{2} + -20k + -6 = 0
Reorder the terms:
-6 + -20k + 50k^{2} = 0
Solving
-6 + -20k + 50k^{2} = 0
Solving for variable 'k'.
Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -10k + 25k^{2}) = 0
Ignore the factor 2.
#### Subproblem 1

Set the factor '(-3 + -10k + 25k^{2})' equal to zero and attempt to solve:
Simplifying
-3 + -10k + 25k^{2} = 0
Solving
-3 + -10k + 25k^{2} = 0
Begin completing the square. Divide all terms by
25 the coefficient of the squared term:
Divide each side by '25'.
-0.12 + -0.4k + k^{2} = 0
Move the constant term to the right:
Add '0.12' to each side of the equation.
-0.12 + -0.4k + 0.12 + k^{2} = 0 + 0.12
Reorder the terms:
-0.12 + 0.12 + -0.4k + k^{2} = 0 + 0.12
Combine like terms: -0.12 + 0.12 = 0.00
0.00 + -0.4k + k^{2} = 0 + 0.12
-0.4k + k^{2} = 0 + 0.12
Combine like terms: 0 + 0.12 = 0.12
-0.4k + k^{2} = 0.12
The k term is -0.4k. Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.
Add '0.04' to each side of the equation.
-0.4k + 0.04 + k^{2} = 0.12 + 0.04
Reorder the terms:
0.04 + -0.4k + k^{2} = 0.12 + 0.04
Combine like terms: 0.12 + 0.04 = 0.16
0.04 + -0.4k + k^{2} = 0.16
Factor a perfect square on the left side:
(k + -0.2)(k + -0.2) = 0.16
Calculate the square root of the right side: 0.4
Break this problem into two subproblems by setting
(k + -0.2) equal to 0.4 and -0.4.
#### Subproblem 1

k + -0.2 = 0.4
Simplifying
k + -0.2 = 0.4
Reorder the terms:
-0.2 + k = 0.4
Solving
-0.2 + k = 0.4
Solving for variable 'k'.
Move all terms containing k to the left, all other terms to the right.
Add '0.2' to each side of the equation.
-0.2 + 0.2 + k = 0.4 + 0.2
Combine like terms: -0.2 + 0.2 = 0.0
0.0 + k = 0.4 + 0.2
k = 0.4 + 0.2
Combine like terms: 0.4 + 0.2 = 0.6
k = 0.6
Simplifying
k = 0.6
#### Subproblem 2

k + -0.2 = -0.4
Simplifying
k + -0.2 = -0.4
Reorder the terms:
-0.2 + k = -0.4
Solving
-0.2 + k = -0.4
Solving for variable 'k'.
Move all terms containing k to the left, all other terms to the right.
Add '0.2' to each side of the equation.
-0.2 + 0.2 + k = -0.4 + 0.2
Combine like terms: -0.2 + 0.2 = 0.0
0.0 + k = -0.4 + 0.2
k = -0.4 + 0.2
Combine like terms: -0.4 + 0.2 = -0.2
k = -0.2
Simplifying
k = -0.2
#### Solution

The solution to the problem is based on the solutions
from the subproblems.
k = {0.6, -0.2}#### Solution

k = {0.6, -0.2}