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Simplifying F(x) = -4x2 + 6x Multiply F * x xF = -4x2 + 6x Reorder the terms: xF = 6x + -4x2 Solving xF = 6x + -4x2 Solving for variable 'x'. Reorder the terms: -6x + xF + 4x2 = 6x + -4x2 + -6x + 4x2 Reorder the terms: -6x + xF + 4x2 = 6x + -6x + -4x2 + 4x2 Combine like terms: 6x + -6x = 0 -6x + xF + 4x2 = 0 + -4x2 + 4x2 -6x + xF + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -6x + xF + 4x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + 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 '(-6 + F + 4x)' equal to zero and attempt to solve: Simplifying -6 + F + 4x = 0 Solving -6 + F + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + F + 6 + 4x = 0 + 6 Reorder the terms: -6 + 6 + F + 4x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + F + 4x = 0 + 6 F + 4x = 0 + 6 Combine like terms: 0 + 6 = 6 F + 4x = 6 Add '-1F' to each side of the equation. F + -1F + 4x = 6 + -1F Combine like terms: F + -1F = 0 0 + 4x = 6 + -1F 4x = 6 + -1F Divide each side by '4'. x = 1.5 + -0.25F Simplifying x = 1.5 + -0.25FSolution
x = {0, 1.5 + -0.25F}
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