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Simplifying F(x) = 130x + -0.2x2 Multiply F * x xF = 130x + -0.2x2 Solving xF = 130x + -0.2x2 Solving for variable 'x'. Reorder the terms: -130x + xF + 0.2x2 = 130x + -0.2x2 + -130x + 0.2x2 Reorder the terms: -130x + xF + 0.2x2 = 130x + -130x + -0.2x2 + 0.2x2 Combine like terms: 130x + -130x = 0 -130x + xF + 0.2x2 = 0 + -0.2x2 + 0.2x2 -130x + xF + 0.2x2 = -0.2x2 + 0.2x2 Combine like terms: -0.2x2 + 0.2x2 = 0.0 -130x + xF + 0.2x2 = 0.0 Factor out the Greatest Common Factor (GCF), 'x'. x(-130 + F + 0.2x) = 0.0Subproblem 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 '(-130 + F + 0.2x)' equal to zero and attempt to solve: Simplifying -130 + F + 0.2x = 0 Solving -130 + F + 0.2x = 0 Move all terms containing x to the left, all other terms to the right. Add '130' to each side of the equation. -130 + F + 130 + 0.2x = 0 + 130 Reorder the terms: -130 + 130 + F + 0.2x = 0 + 130 Combine like terms: -130 + 130 = 0 0 + F + 0.2x = 0 + 130 F + 0.2x = 0 + 130 Combine like terms: 0 + 130 = 130 F + 0.2x = 130 Add '-1F' to each side of the equation. F + -1F + 0.2x = 130 + -1F Combine like terms: F + -1F = 0 0 + 0.2x = 130 + -1F 0.2x = 130 + -1F Divide each side by '0.2'. x = 650 + -5F Simplifying x = 650 + -5FSolution
x = {0, 650 + -5F}
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