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Simplifying F(x) = kx2 + -10kx Multiply F * x xF = kx2 + -10kx Reorder the terms: xF = -10kx + kx2 Solving xF = -10kx + kx2 Solving for variable 'x'. Reorder the terms: 10kx + -1kx2 + xF = -10kx + kx2 + 10kx + -1kx2 Reorder the terms: 10kx + -1kx2 + xF = -10kx + 10kx + kx2 + -1kx2 Combine like terms: -10kx + 10kx = 0 10kx + -1kx2 + xF = 0 + kx2 + -1kx2 10kx + -1kx2 + xF = kx2 + -1kx2 Combine like terms: kx2 + -1kx2 = 0 10kx + -1kx2 + xF = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(10k + -1kx + F) = 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 '(10k + -1kx + F)' equal to zero and attempt to solve: Simplifying 10k + -1kx + F = 0 Reorder the terms: F + 10k + -1kx = 0 Solving F + 10k + -1kx = 0 Move all terms containing x to the left, all other terms to the right. Add '-1F' to each side of the equation. F + 10k + -1F + -1kx = 0 + -1F Reorder the terms: F + -1F + 10k + -1kx = 0 + -1F Combine like terms: F + -1F = 0 0 + 10k + -1kx = 0 + -1F 10k + -1kx = 0 + -1F Remove the zero: 10k + -1kx = -1F Add '-10k' to each side of the equation. 10k + -10k + -1kx = -1F + -10k Combine like terms: 10k + -10k = 0 0 + -1kx = -1F + -10k -1kx = -1F + -10k Divide each side by '-1k'. x = k-1F + 10 Simplifying x = k-1F + 10 Reorder the terms: x = 10 + k-1FSolution
x = {0, 10 + k-1F}
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