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Simplifying 16kx2 + -8kx + k = 0 Reorder the terms: k + -8kx + 16kx2 = 0 Solving k + -8kx + 16kx2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'k'. k(1 + -8x + 16x2) = 0 Factor a trinomial. k((1 + -4x)(1 + -4x)) = 0Subproblem 1
Set the factor 'k' equal to zero and attempt to solve: Simplifying k = 0 Solving k = 0 Move all terms containing k to the left, all other terms to the right. Simplifying k = 0Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Add '4x' to each side of the equation. -4x + 4x = -1 + 4x Combine like terms: -4x + 4x = 0 0 = -1 + 4x Simplifying 0 = -1 + 4x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Add '4x' to each side of the equation. -4x + 4x = -1 + 4x Combine like terms: -4x + 4x = 0 0 = -1 + 4x Simplifying 0 = -1 + 4x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
k = {0}
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