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Simplifying F(x) = 2x2 + x Multiply F * x xF = 2x2 + x Reorder the terms: xF = x + 2x2 Solving xF = x + 2x2 Solving for variable 'x'. Reorder the terms: -1x + xF + -2x2 = x + 2x2 + -1x + -2x2 Reorder the terms: -1x + xF + -2x2 = x + -1x + 2x2 + -2x2 Combine like terms: x + -1x = 0 -1x + xF + -2x2 = 0 + 2x2 + -2x2 -1x + xF + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -1x + xF + -2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + F + -2x) = 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 + -2x)' equal to zero and attempt to solve: Simplifying -1 + F + -2x = 0 Solving -1 + F + -2x = 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 + -2x = 0 + 1 Reorder the terms: -1 + 1 + F + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + F + -2x = 0 + 1 F + -2x = 0 + 1 Combine like terms: 0 + 1 = 1 F + -2x = 1 Add '-1F' to each side of the equation. F + -1F + -2x = 1 + -1F Combine like terms: F + -1F = 0 0 + -2x = 1 + -1F -2x = 1 + -1F Divide each side by '-2'. x = -0.5 + 0.5F Simplifying x = -0.5 + 0.5FSolution
x = {0, -0.5 + 0.5F}
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