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Simplifying 16kxy + -4xy + -2k2xy = 0 Reorder the terms: 16kxy + -2k2xy + -4xy = 0 Solving 16kxy + -2k2xy + -4xy = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2xy'. 2xy(8k + -1k2 + -2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'xy' equal to zero and attempt to solve: Simplifying xy = 0 Solving xy = 0 Move all terms containing k to the left, all other terms to the right. Add '-1xy' to each side of the equation. xy + -1xy = 0 + -1xy Remove the zero: 0 = -1xy Simplifying 0 = -1xy The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(8k + -1k2 + -2)' equal to zero and attempt to solve: Simplifying 8k + -1k2 + -2 = 0 Reorder the terms: -2 + 8k + -1k2 = 0 Solving -2 + 8k + -1k2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -8k + k2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -8k + -2 + k2 = 0 + -2 Reorder the terms: 2 + -2 + -8k + k2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -8k + k2 = 0 + -2 -8k + k2 = 0 + -2 Combine like terms: 0 + -2 = -2 -8k + k2 = -2 The k term is -8k. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8k + 16 + k2 = -2 + 16 Reorder the terms: 16 + -8k + k2 = -2 + 16 Combine like terms: -2 + 16 = 14 16 + -8k + k2 = 14 Factor a perfect square on the left side: (k + -4)(k + -4) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (k + -4) equal to 3.741657387 and -3.741657387.Subproblem 1
k + -4 = 3.741657387 Simplifying k + -4 = 3.741657387 Reorder the terms: -4 + k = 3.741657387 Solving -4 + k = 3.741657387 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + k = 3.741657387 + 4 Combine like terms: -4 + 4 = 0 0 + k = 3.741657387 + 4 k = 3.741657387 + 4 Combine like terms: 3.741657387 + 4 = 7.741657387 k = 7.741657387 Simplifying k = 7.741657387Subproblem 2
k + -4 = -3.741657387 Simplifying k + -4 = -3.741657387 Reorder the terms: -4 + k = -3.741657387 Solving -4 + k = -3.741657387 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + k = -3.741657387 + 4 Combine like terms: -4 + 4 = 0 0 + k = -3.741657387 + 4 k = -3.741657387 + 4 Combine like terms: -3.741657387 + 4 = 0.258342613 k = 0.258342613 Simplifying k = 0.258342613Solution
The solution to the problem is based on the solutions from the subproblems. k = {7.741657387, 0.258342613}Solution
k = {7.741657387, 0.258342613}
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