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Simplifying H(x) = x2 + 2x Multiply H * x xH = x2 + 2x Reorder the terms: xH = 2x + x2 Solving xH = 2x + x2 Solving for variable 'x'. Reorder the terms: -2x + xH + -1x2 = 2x + x2 + -2x + -1x2 Reorder the terms: -2x + xH + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 -2x + xH + -1x2 = 0 + x2 + -1x2 -2x + xH + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -2x + xH + -1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-2 + H + -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 '(-2 + H + -1x)' equal to zero and attempt to solve: Simplifying -2 + H + -1x = 0 Solving -2 + H + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + H + 2 + -1x = 0 + 2 Reorder the terms: -2 + 2 + H + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + H + -1x = 0 + 2 H + -1x = 0 + 2 Combine like terms: 0 + 2 = 2 H + -1x = 2 Add '-1H' to each side of the equation. H + -1H + -1x = 2 + -1H Combine like terms: H + -1H = 0 0 + -1x = 2 + -1H -1x = 2 + -1H Divide each side by '-1'. x = -2 + H Simplifying x = -2 + HSolution
x = {0, -2 + H}
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