(20x+80)H(5.5-x)+(100x-320)H(x-5.5)=2200

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Solution for (20x+80)H(5.5-x)+(100x-320)H(x-5.5)=2200 equation:


Simplifying
(20x + 80) * H(5.5 + -1x) + (100x + -320) * H(x + -5.5) = 2200

Reorder the terms:
(80 + 20x) * H(5.5 + -1x) + (100x + -320) * H(x + -5.5) = 2200

Reorder the terms for easier multiplication:
H(80 + 20x)(5.5 + -1x) + (100x + -320) * H(x + -5.5) = 2200

Multiply (80 + 20x) * (5.5 + -1x)
H(80(5.5 + -1x) + 20x * (5.5 + -1x)) + (100x + -320) * H(x + -5.5) = 2200
H((5.5 * 80 + -1x * 80) + 20x * (5.5 + -1x)) + (100x + -320) * H(x + -5.5) = 2200
H((440 + -80x) + 20x * (5.5 + -1x)) + (100x + -320) * H(x + -5.5) = 2200
H(440 + -80x + (5.5 * 20x + -1x * 20x)) + (100x + -320) * H(x + -5.5) = 2200
H(440 + -80x + (110x + -20x2)) + (100x + -320) * H(x + -5.5) = 2200

Combine like terms: -80x + 110x = 30x
H(440 + 30x + -20x2) + (100x + -320) * H(x + -5.5) = 2200
(440 * H + 30x * H + -20x2 * H) + (100x + -320) * H(x + -5.5) = 2200
(440H + 30xH + -20x2H) + (100x + -320) * H(x + -5.5) = 2200

Reorder the terms:
440H + 30xH + -20x2H + (-320 + 100x) * H(x + -5.5) = 2200

Reorder the terms:
440H + 30xH + -20x2H + (-320 + 100x) * H(-5.5 + x) = 2200

Reorder the terms for easier multiplication:
440H + 30xH + -20x2H + H(-320 + 100x)(-5.5 + x) = 2200

Multiply (-320 + 100x) * (-5.5 + x)
440H + 30xH + -20x2H + H(-320(-5.5 + x) + 100x * (-5.5 + x)) = 2200
440H + 30xH + -20x2H + H((-5.5 * -320 + x * -320) + 100x * (-5.5 + x)) = 2200
440H + 30xH + -20x2H + H((1760 + -320x) + 100x * (-5.5 + x)) = 2200
440H + 30xH + -20x2H + H(1760 + -320x + (-5.5 * 100x + x * 100x)) = 2200
440H + 30xH + -20x2H + H(1760 + -320x + (-550x + 100x2)) = 2200

Combine like terms: -320x + -550x = -870x
440H + 30xH + -20x2H + H(1760 + -870x + 100x2) = 2200
440H + 30xH + -20x2H + (1760 * H + -870x * H + 100x2 * H) = 2200
440H + 30xH + -20x2H + (1760H + -870xH + 100x2H) = 2200

Reorder the terms:
440H + 1760H + 30xH + -870xH + -20x2H + 100x2H = 2200

Combine like terms: 440H + 1760H = 2200H
2200H + 30xH + -870xH + -20x2H + 100x2H = 2200

Combine like terms: 30xH + -870xH = -840xH
2200H + -840xH + -20x2H + 100x2H = 2200

Combine like terms: -20x2H + 100x2H = 80x2H
2200H + -840xH + 80x2H = 2200

Solving
2200H + -840xH + 80x2H = 2200

Solving for variable 'H'.

Move all terms containing H to the left, all other terms to the right.

Reorder the terms:
-2200 + 2200H + -840xH + 80x2H = 2200 + -2200

Combine like terms: 2200 + -2200 = 0
-2200 + 2200H + -840xH + 80x2H = 0

Factor out the Greatest Common Factor (GCF), '40'.
40(-55 + 55H + -21xH + 2x2H) = 0

Ignore the factor 40.

Subproblem 1

Set the factor '(-55 + 55H + -21xH + 2x2H)' equal to zero and attempt to solve: Simplifying -55 + 55H + -21xH + 2x2H = 0 Solving -55 + 55H + -21xH + 2x2H = 0 Move all terms containing H to the left, all other terms to the right. Add '55' to each side of the equation. -55 + 55H + -21xH + 55 + 2x2H = 0 + 55 Reorder the terms: -55 + 55 + 55H + -21xH + 2x2H = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 55H + -21xH + 2x2H = 0 + 55 55H + -21xH + 2x2H = 0 + 55 Combine like terms: 0 + 55 = 55 55H + -21xH + 2x2H = 55 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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