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Simplifying H(x) = 180x + -5x2 Multiply H * x xH = 180x + -5x2 Solving xH = 180x + -5x2 Solving for variable 'x'. Reorder the terms: -180x + xH + 5x2 = 180x + -5x2 + -180x + 5x2 Reorder the terms: -180x + xH + 5x2 = 180x + -180x + -5x2 + 5x2 Combine like terms: 180x + -180x = 0 -180x + xH + 5x2 = 0 + -5x2 + 5x2 -180x + xH + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -180x + xH + 5x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-180 + 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 '(-180 + H + 5x)' equal to zero and attempt to solve: Simplifying -180 + H + 5x = 0 Solving -180 + H + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '180' to each side of the equation. -180 + H + 180 + 5x = 0 + 180 Reorder the terms: -180 + 180 + H + 5x = 0 + 180 Combine like terms: -180 + 180 = 0 0 + H + 5x = 0 + 180 H + 5x = 0 + 180 Combine like terms: 0 + 180 = 180 H + 5x = 180 Add '-1H' to each side of the equation. H + -1H + 5x = 180 + -1H Combine like terms: H + -1H = 0 0 + 5x = 180 + -1H 5x = 180 + -1H Divide each side by '5'. x = 36 + -0.2H Simplifying x = 36 + -0.2HSolution
x = {0, 36 + -0.2H}
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