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Simplifying 2kx2 + kx + k = 0 Reorder the terms: k + kx + 2kx2 = 0 Solving k + kx + 2kx2 = 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 + x + 2x2) = 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 + x + 2x2)' equal to zero and attempt to solve: Simplifying 1 + x + 2x2 = 0 Solving 1 + x + 2x2 = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + x + -1 + 2x2 = 0 + -1 Reorder the terms: 1 + -1 + x + 2x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x + 2x2 = 0 + -1 x + 2x2 = 0 + -1 Combine like terms: 0 + -1 = -1 x + 2x2 = -1 Add '-1x' to each side of the equation. x + -1x + 2x2 = -1 + -1x Combine like terms: x + -1x = 0 0 + 2x2 = -1 + -1x 2x2 = -1 + -1x Add '-2x2' to each side of the equation. 2x2 + -2x2 = -1 + -1x + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 = -1 + -1x + -2x2 Simplifying 0 = -1 + -1x + -2x2 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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