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Simplifying G(x) = x2 + -36x Multiply G * x xG = x2 + -36x Reorder the terms: xG = -36x + x2 Solving xG = -36x + x2 Solving for variable 'x'. Reorder the terms: 36x + xG + -1x2 = -36x + x2 + 36x + -1x2 Reorder the terms: 36x + xG + -1x2 = -36x + 36x + x2 + -1x2 Combine like terms: -36x + 36x = 0 36x + xG + -1x2 = 0 + x2 + -1x2 36x + xG + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 36x + xG + -1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(36 + G + -1x) = 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 '(36 + G + -1x)' equal to zero and attempt to solve: Simplifying 36 + G + -1x = 0 Solving 36 + G + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + G + -36 + -1x = 0 + -36 Reorder the terms: 36 + -36 + G + -1x = 0 + -36 Combine like terms: 36 + -36 = 0 0 + G + -1x = 0 + -36 G + -1x = 0 + -36 Combine like terms: 0 + -36 = -36 G + -1x = -36 Add '-1G' to each side of the equation. G + -1G + -1x = -36 + -1G Combine like terms: G + -1G = 0 0 + -1x = -36 + -1G -1x = -36 + -1G Divide each side by '-1'. x = 36 + G Simplifying x = 36 + GSolution
x = {0, 36 + G}
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