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Simplifying
50k2 + -20k + -6 = 0

Reorder the terms:
-6 + -20k + 50k2 = 0

Solving
-6 + -20k + 50k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -10k + 25k2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-3 + -10k + 25k2)' equal to zero and attempt to solve: Simplifying -3 + -10k + 25k2 = 0 Solving -3 + -10k + 25k2 = 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 + k2 = 0 Move the constant term to the right: Add '0.12' to each side of the equation. -0.12 + -0.4k + 0.12 + k2 = 0 + 0.12 Reorder the terms: -0.12 + 0.12 + -0.4k + k2 = 0 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + -0.4k + k2 = 0 + 0.12 -0.4k + k2 = 0 + 0.12 Combine like terms: 0 + 0.12 = 0.12 -0.4k + k2 = 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 + k2 = 0.12 + 0.04 Reorder the terms: 0.04 + -0.4k + k2 = 0.12 + 0.04 Combine like terms: 0.12 + 0.04 = 0.16 0.04 + -0.4k + k2 = 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}
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