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Simplifying H(x) = x2 + 9x Multiply H * x xH = x2 + 9x Reorder the terms: xH = 9x + x2 Solving xH = 9x + x2 Solving for variable 'x'. Reorder the terms: -9x + xH + -1x2 = 9x + x2 + -9x + -1x2 Reorder the terms: -9x + xH + -1x2 = 9x + -9x + x2 + -1x2 Combine like terms: 9x + -9x = 0 -9x + xH + -1x2 = 0 + x2 + -1x2 -9x + xH + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -9x + xH + -1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-9 + 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 '(-9 + H + -1x)' equal to zero and attempt to solve: Simplifying -9 + H + -1x = 0 Solving -9 + H + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + H + 9 + -1x = 0 + 9 Reorder the terms: -9 + 9 + H + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + H + -1x = 0 + 9 H + -1x = 0 + 9 Combine like terms: 0 + 9 = 9 H + -1x = 9 Add '-1H' to each side of the equation. H + -1H + -1x = 9 + -1H Combine like terms: H + -1H = 0 0 + -1x = 9 + -1H -1x = 9 + -1H Divide each side by '-1'. x = -9 + H Simplifying x = -9 + HSolution
x = {0, -9 + H}
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