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Simplifying H(x) = 5x2 + -35x Multiply H * x xH = 5x2 + -35x Reorder the terms: xH = -35x + 5x2 Solving xH = -35x + 5x2 Solving for variable 'x'. Reorder the terms: 35x + xH + -5x2 = -35x + 5x2 + 35x + -5x2 Reorder the terms: 35x + xH + -5x2 = -35x + 35x + 5x2 + -5x2 Combine like terms: -35x + 35x = 0 35x + xH + -5x2 = 0 + 5x2 + -5x2 35x + xH + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 35x + xH + -5x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(35 + H + -5x) = 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 '(35 + H + -5x)' equal to zero and attempt to solve: Simplifying 35 + H + -5x = 0 Solving 35 + H + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + H + -35 + -5x = 0 + -35 Reorder the terms: 35 + -35 + H + -5x = 0 + -35 Combine like terms: 35 + -35 = 0 0 + H + -5x = 0 + -35 H + -5x = 0 + -35 Combine like terms: 0 + -35 = -35 H + -5x = -35 Add '-1H' to each side of the equation. H + -1H + -5x = -35 + -1H Combine like terms: H + -1H = 0 0 + -5x = -35 + -1H -5x = -35 + -1H Divide each side by '-5'. x = 7 + 0.2H Simplifying x = 7 + 0.2HSolution
x = {0, 7 + 0.2H}
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