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Simplifying H(x) = 4x2 + -2x Multiply H * x xH = 4x2 + -2x Reorder the terms: xH = -2x + 4x2 Solving xH = -2x + 4x2 Solving for variable 'x'. Reorder the terms: 2x + xH + -4x2 = -2x + 4x2 + 2x + -4x2 Reorder the terms: 2x + xH + -4x2 = -2x + 2x + 4x2 + -4x2 Combine like terms: -2x + 2x = 0 2x + xH + -4x2 = 0 + 4x2 + -4x2 2x + xH + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 2x + xH + -4x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(2 + H + -4x) = 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 + -4x)' equal to zero and attempt to solve: Simplifying 2 + H + -4x = 0 Solving 2 + H + -4x = 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 + -4x = 0 + -2 Reorder the terms: 2 + -2 + H + -4x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + H + -4x = 0 + -2 H + -4x = 0 + -2 Combine like terms: 0 + -2 = -2 H + -4x = -2 Add '-1H' to each side of the equation. H + -1H + -4x = -2 + -1H Combine like terms: H + -1H = 0 0 + -4x = -2 + -1H -4x = -2 + -1H Divide each side by '-4'. x = 0.5 + 0.25H Simplifying x = 0.5 + 0.25HSolution
x = {0, 0.5 + 0.25H}
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