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Simplifying F(x) = 4x2 + 32x Multiply F * x xF = 4x2 + 32x Reorder the terms: xF = 32x + 4x2 Solving xF = 32x + 4x2 Solving for variable 'x'. Reorder the terms: -32x + xF + -4x2 = 32x + 4x2 + -32x + -4x2 Reorder the terms: -32x + xF + -4x2 = 32x + -32x + 4x2 + -4x2 Combine like terms: 32x + -32x = 0 -32x + xF + -4x2 = 0 + 4x2 + -4x2 -32x + xF + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -32x + xF + -4x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-32 + 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 '(-32 + F + -4x)' equal to zero and attempt to solve: Simplifying -32 + F + -4x = 0 Solving -32 + F + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '32' to each side of the equation. -32 + F + 32 + -4x = 0 + 32 Reorder the terms: -32 + 32 + F + -4x = 0 + 32 Combine like terms: -32 + 32 = 0 0 + F + -4x = 0 + 32 F + -4x = 0 + 32 Combine like terms: 0 + 32 = 32 F + -4x = 32 Add '-1F' to each side of the equation. F + -1F + -4x = 32 + -1F Combine like terms: F + -1F = 0 0 + -4x = 32 + -1F -4x = 32 + -1F Divide each side by '-4'. x = -8 + 0.25F Simplifying x = -8 + 0.25FSolution
x = {0, -8 + 0.25F}
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