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Simplifying (20x + 80) * H(5.5 + -1x) + (100x + -320) * H(x + -5.5) = 660 Reorder the terms: (80 + 20x) * H(5.5 + -1x) + (100x + -320) * H(x + -5.5) = 660 Reorder the terms for easier multiplication: H(80 + 20x)(5.5 + -1x) + (100x + -320) * H(x + -5.5) = 660 Multiply (80 + 20x) * (5.5 + -1x) H(80(5.5 + -1x) + 20x * (5.5 + -1x)) + (100x + -320) * H(x + -5.5) = 660 H((5.5 * 80 + -1x * 80) + 20x * (5.5 + -1x)) + (100x + -320) * H(x + -5.5) = 660 H((440 + -80x) + 20x * (5.5 + -1x)) + (100x + -320) * H(x + -5.5) = 660 H(440 + -80x + (5.5 * 20x + -1x * 20x)) + (100x + -320) * H(x + -5.5) = 660 H(440 + -80x + (110x + -20x2)) + (100x + -320) * H(x + -5.5) = 660 Combine like terms: -80x + 110x = 30x H(440 + 30x + -20x2) + (100x + -320) * H(x + -5.5) = 660 (440 * H + 30x * H + -20x2 * H) + (100x + -320) * H(x + -5.5) = 660 (440H + 30xH + -20x2H) + (100x + -320) * H(x + -5.5) = 660 Reorder the terms: 440H + 30xH + -20x2H + (-320 + 100x) * H(x + -5.5) = 660 Reorder the terms: 440H + 30xH + -20x2H + (-320 + 100x) * H(-5.5 + x) = 660 Reorder the terms for easier multiplication: 440H + 30xH + -20x2H + H(-320 + 100x)(-5.5 + x) = 660 Multiply (-320 + 100x) * (-5.5 + x) 440H + 30xH + -20x2H + H(-320(-5.5 + x) + 100x * (-5.5 + x)) = 660 440H + 30xH + -20x2H + H((-5.5 * -320 + x * -320) + 100x * (-5.5 + x)) = 660 440H + 30xH + -20x2H + H((1760 + -320x) + 100x * (-5.5 + x)) = 660 440H + 30xH + -20x2H + H(1760 + -320x + (-5.5 * 100x + x * 100x)) = 660 440H + 30xH + -20x2H + H(1760 + -320x + (-550x + 100x2)) = 660 Combine like terms: -320x + -550x = -870x 440H + 30xH + -20x2H + H(1760 + -870x + 100x2) = 660 440H + 30xH + -20x2H + (1760 * H + -870x * H + 100x2 * H) = 660 440H + 30xH + -20x2H + (1760H + -870xH + 100x2H) = 660 Reorder the terms: 440H + 1760H + 30xH + -870xH + -20x2H + 100x2H = 660 Combine like terms: 440H + 1760H = 2200H 2200H + 30xH + -870xH + -20x2H + 100x2H = 660 Combine like terms: 30xH + -870xH = -840xH 2200H + -840xH + -20x2H + 100x2H = 660 Combine like terms: -20x2H + 100x2H = 80x2H 2200H + -840xH + 80x2H = 660 Solving 2200H + -840xH + 80x2H = 660 Solving for variable 'H'. Move all terms containing H to the left, all other terms to the right. Reorder the terms: -660 + 2200H + -840xH + 80x2H = 660 + -660 Combine like terms: 660 + -660 = 0 -660 + 2200H + -840xH + 80x2H = 0 Factor out the Greatest Common Factor (GCF), '20'. 20(-33 + 110H + -42xH + 4x2H) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(-33 + 110H + -42xH + 4x2H)' equal to zero and attempt to solve: Simplifying -33 + 110H + -42xH + 4x2H = 0 Solving -33 + 110H + -42xH + 4x2H = 0 Move all terms containing H to the left, all other terms to the right. Add '33' to each side of the equation. -33 + 110H + -42xH + 33 + 4x2H = 0 + 33 Reorder the terms: -33 + 33 + 110H + -42xH + 4x2H = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 110H + -42xH + 4x2H = 0 + 33 110H + -42xH + 4x2H = 0 + 33 Combine like terms: 0 + 33 = 33 110H + -42xH + 4x2H = 33 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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