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Simplifying H(x) = -0.005x2 + 0.25x Multiply H * x xH = -0.005x2 + 0.25x Reorder the terms: xH = 0.25x + -0.005x2 Solving xH = 0.25x + -0.005x2 Solving for variable 'x'. Reorder the terms: -0.25x + xH + 0.005x2 = 0.25x + -0.005x2 + -0.25x + 0.005x2 Reorder the terms: -0.25x + xH + 0.005x2 = 0.25x + -0.25x + -0.005x2 + 0.005x2 Combine like terms: 0.25x + -0.25x = 0.00 -0.25x + xH + 0.005x2 = 0.00 + -0.005x2 + 0.005x2 -0.25x + xH + 0.005x2 = -0.005x2 + 0.005x2 Combine like terms: -0.005x2 + 0.005x2 = 0.000 -0.25x + xH + 0.005x2 = 0.000 Factor out the Greatest Common Factor (GCF), 'x'. x(-0.25 + H + 0.005x) = 0.000Subproblem 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 '(-0.25 + H + 0.005x)' equal to zero and attempt to solve: Simplifying -0.25 + H + 0.005x = 0 Solving -0.25 + H + 0.005x = 0 Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + H + 0.25 + 0.005x = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + H + 0.005x = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + H + 0.005x = 0 + 0.25 H + 0.005x = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 H + 0.005x = 0.25 Add '-1H' to each side of the equation. H + -1H + 0.005x = 0.25 + -1H Combine like terms: H + -1H = 0 0 + 0.005x = 0.25 + -1H 0.005x = 0.25 + -1H Divide each side by '0.005'. x = 50 + -200H Simplifying x = 50 + -200HSolution
x = {0, 50 + -200H}
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