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Simplifying x3 = 2kx2 + -1k2x Solving x3 = 2kx2 + -1k2x Solving for variable 'x'. Reorder the terms: -2kx2 + k2x + x3 = 2kx2 + -1k2x + -2kx2 + k2x Reorder the terms: -2kx2 + k2x + x3 = 2kx2 + -2kx2 + -1k2x + k2x Combine like terms: 2kx2 + -2kx2 = 0 -2kx2 + k2x + x3 = 0 + -1k2x + k2x -2kx2 + k2x + x3 = -1k2x + k2x Combine like terms: -1k2x + k2x = 0 -2kx2 + k2x + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-2kx + k2 + x2) = 0 Factor a trinomial. x((k + -1x)(k + -1x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(k + -1x)' equal to zero and attempt to solve: Simplifying k + -1x = 0 Solving k + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1k' to each side of the equation. k + -1k + -1x = 0 + -1k Combine like terms: k + -1k = 0 0 + -1x = 0 + -1k -1x = 0 + -1k Remove the zero: -1x = -1k Divide each side by '-1'. x = k Simplifying x = kSubproblem 3
Set the factor '(k + -1x)' equal to zero and attempt to solve: Simplifying k + -1x = 0 Solving k + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1k' to each side of the equation. k + -1k + -1x = 0 + -1k Combine like terms: k + -1k = 0 0 + -1x = 0 + -1k -1x = 0 + -1k Remove the zero: -1x = -1k Divide each side by '-1'. x = k Simplifying x = kSolution
x = {0, k, k}
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