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