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Simplifying F(x) = -1x2 + 40x Multiply F * x xF = -1x2 + 40x Reorder the terms: xF = 40x + -1x2 Solving xF = 40x + -1x2 Solving for variable 'x'. Reorder the terms: -40x + xF + x2 = 40x + -1x2 + -40x + x2 Reorder the terms: -40x + xF + x2 = 40x + -40x + -1x2 + x2 Combine like terms: 40x + -40x = 0 -40x + xF + x2 = 0 + -1x2 + x2 -40x + xF + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -40x + xF + x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-40 + F + x) = 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 '(-40 + F + x)' equal to zero and attempt to solve: Simplifying -40 + F + x = 0 Solving -40 + F + x = 0 Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + F + 40 + x = 0 + 40 Reorder the terms: -40 + 40 + F + x = 0 + 40 Combine like terms: -40 + 40 = 0 0 + F + x = 0 + 40 F + x = 0 + 40 Combine like terms: 0 + 40 = 40 F + x = 40 Add '-1F' to each side of the equation. F + -1F + x = 40 + -1F Combine like terms: F + -1F = 0 0 + x = 40 + -1F x = 40 + -1F Simplifying x = 40 + -1FSolution
x = {0, 40 + -1F}
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