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Simplifying K(x) = 4x + -5x2 Multiply K * x xK = 4x + -5x2 Solving xK = 4x + -5x2 Solving for variable 'x'. Reorder the terms: -4x + xK + 5x2 = 4x + -5x2 + -4x + 5x2 Reorder the terms: -4x + xK + 5x2 = 4x + -4x + -5x2 + 5x2 Combine like terms: 4x + -4x = 0 -4x + xK + 5x2 = 0 + -5x2 + 5x2 -4x + xK + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -4x + xK + 5x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + K + 5x) = 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 '(-4 + K + 5x)' equal to zero and attempt to solve: Simplifying -4 + K + 5x = 0 Solving -4 + K + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + K + 4 + 5x = 0 + 4 Reorder the terms: -4 + 4 + K + 5x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + K + 5x = 0 + 4 K + 5x = 0 + 4 Combine like terms: 0 + 4 = 4 K + 5x = 4 Add '-1K' to each side of the equation. K + -1K + 5x = 4 + -1K Combine like terms: K + -1K = 0 0 + 5x = 4 + -1K 5x = 4 + -1K Divide each side by '5'. x = 0.8 + -0.2K Simplifying x = 0.8 + -0.2KSolution
x = {0, 0.8 + -0.2K}
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