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Simplifying G(x) = x2 + 11x Multiply G * x xG = x2 + 11x Reorder the terms: xG = 11x + x2 Solving xG = 11x + x2 Solving for variable 'x'. Reorder the terms: -11x + xG + -1x2 = 11x + x2 + -11x + -1x2 Reorder the terms: -11x + xG + -1x2 = 11x + -11x + x2 + -1x2 Combine like terms: 11x + -11x = 0 -11x + xG + -1x2 = 0 + x2 + -1x2 -11x + xG + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -11x + xG + -1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-11 + 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 '(-11 + G + -1x)' equal to zero and attempt to solve: Simplifying -11 + G + -1x = 0 Solving -11 + G + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + G + 11 + -1x = 0 + 11 Reorder the terms: -11 + 11 + G + -1x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + G + -1x = 0 + 11 G + -1x = 0 + 11 Combine like terms: 0 + 11 = 11 G + -1x = 11 Add '-1G' to each side of the equation. G + -1G + -1x = 11 + -1G Combine like terms: G + -1G = 0 0 + -1x = 11 + -1G -1x = 11 + -1G Divide each side by '-1'. x = -11 + G Simplifying x = -11 + GSolution
x = {0, -11 + G}
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