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

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


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

Multiply f * x
fx = (20x + 80) * H(5.5 + -1x) + (100x + -320) * H(x + -5.5)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 2200x-1H + -840H + 80xH

Simplifying
f = 2200x-1H + -840H + 80xH

Reorder the terms:
f = -840H + 2200x-1H + 80xH

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