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Simplifying F(x) = 4x2 + -1x Multiply F * x xF = 4x2 + -1x Reorder the terms: xF = -1x + 4x2 Solving xF = -1x + 4x2 Solving for variable 'x'. Reorder the terms: x + xF + -4x2 = -1x + 4x2 + x + -4x2 Reorder the terms: x + xF + -4x2 = -1x + x + 4x2 + -4x2 Combine like terms: -1x + x = 0 x + xF + -4x2 = 0 + 4x2 + -4x2 x + xF + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 x + xF + -4x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(1 + F + -4x) = 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 '(1 + F + -4x)' equal to zero and attempt to solve: Simplifying 1 + F + -4x = 0 Solving 1 + F + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + F + -1 + -4x = 0 + -1 Reorder the terms: 1 + -1 + F + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + F + -4x = 0 + -1 F + -4x = 0 + -1 Combine like terms: 0 + -1 = -1 F + -4x = -1 Add '-1F' to each side of the equation. F + -1F + -4x = -1 + -1F Combine like terms: F + -1F = 0 0 + -4x = -1 + -1F -4x = -1 + -1F Divide each side by '-4'. x = 0.25 + 0.25F Simplifying x = 0.25 + 0.25FSolution
x = {0, 0.25 + 0.25F}
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