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Simplifying H(x) = -1x2 + 4x Multiply H * x xH = -1x2 + 4x Reorder the terms: xH = 4x + -1x2 Solving xH = 4x + -1x2 Solving for variable 'x'. Reorder the terms: -4x + xH + x2 = 4x + -1x2 + -4x + x2 Reorder the terms: -4x + xH + x2 = 4x + -4x + -1x2 + x2 Combine like terms: 4x + -4x = 0 -4x + xH + x2 = 0 + -1x2 + x2 -4x + xH + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -4x + xH + x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + H + x) = 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 '(-4 + H + x)' equal to zero and attempt to solve: Simplifying -4 + H + x = 0 Solving -4 + H + x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + H + 4 + x = 0 + 4 Reorder the terms: -4 + 4 + H + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + H + x = 0 + 4 H + x = 0 + 4 Combine like terms: 0 + 4 = 4 H + x = 4 Add '-1H' to each side of the equation. H + -1H + x = 4 + -1H Combine like terms: H + -1H = 0 0 + x = 4 + -1H x = 4 + -1H Simplifying x = 4 + -1HSolution
x = {0, 4 + -1H}
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