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Simplifying F(x) = 4x2 + 24x Multiply F * x xF = 4x2 + 24x Reorder the terms: xF = 24x + 4x2 Solving xF = 24x + 4x2 Solving for variable 'x'. Reorder the terms: -24x + xF + -4x2 = 24x + 4x2 + -24x + -4x2 Reorder the terms: -24x + xF + -4x2 = 24x + -24x + 4x2 + -4x2 Combine like terms: 24x + -24x = 0 -24x + xF + -4x2 = 0 + 4x2 + -4x2 -24x + xF + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -24x + xF + -4x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-24 + 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 '(-24 + F + -4x)' equal to zero and attempt to solve: Simplifying -24 + F + -4x = 0 Solving -24 + F + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + F + 24 + -4x = 0 + 24 Reorder the terms: -24 + 24 + F + -4x = 0 + 24 Combine like terms: -24 + 24 = 0 0 + F + -4x = 0 + 24 F + -4x = 0 + 24 Combine like terms: 0 + 24 = 24 F + -4x = 24 Add '-1F' to each side of the equation. F + -1F + -4x = 24 + -1F Combine like terms: F + -1F = 0 0 + -4x = 24 + -1F -4x = 24 + -1F Divide each side by '-4'. x = -6 + 0.25F Simplifying x = -6 + 0.25FSolution
x = {0, -6 + 0.25F}
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