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Simplifying G(x) = 5x2 + -8x Multiply G * x xG = 5x2 + -8x Reorder the terms: xG = -8x + 5x2 Solving xG = -8x + 5x2 Solving for variable 'x'. Reorder the terms: 8x + xG + -5x2 = -8x + 5x2 + 8x + -5x2 Reorder the terms: 8x + xG + -5x2 = -8x + 8x + 5x2 + -5x2 Combine like terms: -8x + 8x = 0 8x + xG + -5x2 = 0 + 5x2 + -5x2 8x + xG + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 8x + xG + -5x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(8 + G + -5x) = 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 '(8 + G + -5x)' equal to zero and attempt to solve: Simplifying 8 + G + -5x = 0 Solving 8 + G + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + G + -8 + -5x = 0 + -8 Reorder the terms: 8 + -8 + G + -5x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + G + -5x = 0 + -8 G + -5x = 0 + -8 Combine like terms: 0 + -8 = -8 G + -5x = -8 Add '-1G' to each side of the equation. G + -1G + -5x = -8 + -1G Combine like terms: G + -1G = 0 0 + -5x = -8 + -1G -5x = -8 + -1G Divide each side by '-5'. x = 1.6 + 0.2G Simplifying x = 1.6 + 0.2GSolution
x = {0, 1.6 + 0.2G}
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