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Simplifying F(x) = 4x2 + -12x2 + -16x Multiply F * x xF = 4x2 + -12x2 + -16x Reorder the terms: xF = -16x + 4x2 + -12x2 Combine like terms: 4x2 + -12x2 = -8x2 xF = -16x + -8x2 Solving xF = -16x + -8x2 Solving for variable 'x'. Reorder the terms: 16x + xF + 8x2 = -16x + -8x2 + 16x + 8x2 Reorder the terms: 16x + xF + 8x2 = -16x + 16x + -8x2 + 8x2 Combine like terms: -16x + 16x = 0 16x + xF + 8x2 = 0 + -8x2 + 8x2 16x + xF + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 16x + xF + 8x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(16 + F + 8x) = 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 '(16 + F + 8x)' equal to zero and attempt to solve: Simplifying 16 + F + 8x = 0 Solving 16 + F + 8x = 0 Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + F + -16 + 8x = 0 + -16 Reorder the terms: 16 + -16 + F + 8x = 0 + -16 Combine like terms: 16 + -16 = 0 0 + F + 8x = 0 + -16 F + 8x = 0 + -16 Combine like terms: 0 + -16 = -16 F + 8x = -16 Add '-1F' to each side of the equation. F + -1F + 8x = -16 + -1F Combine like terms: F + -1F = 0 0 + 8x = -16 + -1F 8x = -16 + -1F Divide each side by '8'. x = -2 + -0.125F Simplifying x = -2 + -0.125FSolution
x = {0, -2 + -0.125F}
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