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Simplifying K(x) = x2 + -2x Multiply K * x xK = x2 + -2x Reorder the terms: xK = -2x + x2 Solving xK = -2x + x2 Solving for variable 'x'. Reorder the terms: 2x + xK + -1x2 = -2x + x2 + 2x + -1x2 Reorder the terms: 2x + xK + -1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 2x + xK + -1x2 = 0 + x2 + -1x2 2x + xK + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 2x + xK + -1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(2 + 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 '(2 + K + -1x)' equal to zero and attempt to solve: Simplifying 2 + K + -1x = 0 Solving 2 + K + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + K + -2 + -1x = 0 + -2 Reorder the terms: 2 + -2 + K + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + K + -1x = 0 + -2 K + -1x = 0 + -2 Combine like terms: 0 + -2 = -2 K + -1x = -2 Add '-1K' to each side of the equation. K + -1K + -1x = -2 + -1K Combine like terms: K + -1K = 0 0 + -1x = -2 + -1K -1x = -2 + -1K Divide each side by '-1'. x = 2 + K Simplifying x = 2 + KSolution
x = {0, 2 + K}
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