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Simplifying F(x) = 100x + -5x2 Multiply F * x xF = 100x + -5x2 Solving xF = 100x + -5x2 Solving for variable 'x'. Reorder the terms: -100x + xF + 5x2 = 100x + -5x2 + -100x + 5x2 Reorder the terms: -100x + xF + 5x2 = 100x + -100x + -5x2 + 5x2 Combine like terms: 100x + -100x = 0 -100x + xF + 5x2 = 0 + -5x2 + 5x2 -100x + xF + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -100x + xF + 5x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-100 + F + 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 '(-100 + F + 5x)' equal to zero and attempt to solve: Simplifying -100 + F + 5x = 0 Solving -100 + F + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + F + 100 + 5x = 0 + 100 Reorder the terms: -100 + 100 + F + 5x = 0 + 100 Combine like terms: -100 + 100 = 0 0 + F + 5x = 0 + 100 F + 5x = 0 + 100 Combine like terms: 0 + 100 = 100 F + 5x = 100 Add '-1F' to each side of the equation. F + -1F + 5x = 100 + -1F Combine like terms: F + -1F = 0 0 + 5x = 100 + -1F 5x = 100 + -1F Divide each side by '5'. x = 20 + -0.2F Simplifying x = 20 + -0.2FSolution
x = {0, 20 + -0.2F}
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