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Simplifying 0 = (50x + -80x * i)(80 + -1i(50 + -1x)) Multiply x * i 0 = (50x + -80ix)(80 + -1i(50 + -1x)) Reorder the terms: 0 = (-80ix + 50x)(80 + -1i(50 + -1x)) 0 = (-80ix + 50x)(80 + (50 * -1i + -1x * -1i)) 0 = (-80ix + 50x)(80 + (-50i + 1ix)) Multiply (-80ix + 50x) * (80 + -50i + 1ix) 0 = (-80ix * (80 + -50i + 1ix) + 50x * (80 + -50i + 1ix)) 0 = ((80 * -80ix + -50i * -80ix + 1ix * -80ix) + 50x * (80 + -50i + 1ix)) 0 = ((-6400ix + 4000i2x + -80i2x2) + 50x * (80 + -50i + 1ix)) 0 = (-6400ix + 4000i2x + -80i2x2 + (80 * 50x + -50i * 50x + 1ix * 50x)) Reorder the terms: 0 = (-6400ix + 4000i2x + -80i2x2 + (-2500ix + 50ix2 + 4000x)) 0 = (-6400ix + 4000i2x + -80i2x2 + (-2500ix + 50ix2 + 4000x)) Reorder the terms: 0 = (-6400ix + -2500ix + 50ix2 + 4000i2x + -80i2x2 + 4000x) Combine like terms: -6400ix + -2500ix = -8900ix 0 = (-8900ix + 50ix2 + 4000i2x + -80i2x2 + 4000x) Solving 0 = -8900ix + 50ix2 + 4000i2x + -80i2x2 + 4000x Solving for variable 'i'. Remove the zero: 8900ix + -50ix2 + -4000i2x + 80i2x2 + -4000x = -8900ix + 50ix2 + 4000i2x + -80i2x2 + 4000x + 8900ix + -50ix2 + -4000i2x + 80i2x2 + -4000x Reorder the terms: 8900ix + -50ix2 + -4000i2x + 80i2x2 + -4000x = -8900ix + 8900ix + 50ix2 + -50ix2 + 4000i2x + -4000i2x + -80i2x2 + 80i2x2 + 4000x + -4000x Combine like terms: -8900ix + 8900ix = 0 8900ix + -50ix2 + -4000i2x + 80i2x2 + -4000x = 0 + 50ix2 + -50ix2 + 4000i2x + -4000i2x + -80i2x2 + 80i2x2 + 4000x + -4000x 8900ix + -50ix2 + -4000i2x + 80i2x2 + -4000x = 50ix2 + -50ix2 + 4000i2x + -4000i2x + -80i2x2 + 80i2x2 + 4000x + -4000x Combine like terms: 50ix2 + -50ix2 = 0 8900ix + -50ix2 + -4000i2x + 80i2x2 + -4000x = 0 + 4000i2x + -4000i2x + -80i2x2 + 80i2x2 + 4000x + -4000x 8900ix + -50ix2 + -4000i2x + 80i2x2 + -4000x = 4000i2x + -4000i2x + -80i2x2 + 80i2x2 + 4000x + -4000x Combine like terms: 4000i2x + -4000i2x = 0 8900ix + -50ix2 + -4000i2x + 80i2x2 + -4000x = 0 + -80i2x2 + 80i2x2 + 4000x + -4000x 8900ix + -50ix2 + -4000i2x + 80i2x2 + -4000x = -80i2x2 + 80i2x2 + 4000x + -4000x Combine like terms: -80i2x2 + 80i2x2 = 0 8900ix + -50ix2 + -4000i2x + 80i2x2 + -4000x = 0 + 4000x + -4000x 8900ix + -50ix2 + -4000i2x + 80i2x2 + -4000x = 4000x + -4000x Combine like terms: 4000x + -4000x = 0 8900ix + -50ix2 + -4000i2x + 80i2x2 + -4000x = 0 Factor out the Greatest Common Factor (GCF), '10x'. 10x(890i + -5ix + -400i2 + 8i2x + -400) = 0 Ignore the factor 10.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing i to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(890i + -5ix + -400i2 + 8i2x + -400)' equal to zero and attempt to solve: Simplifying 890i + -5ix + -400i2 + 8i2x + -400 = 0 Reorder the terms: -400 + 890i + -5ix + -400i2 + 8i2x = 0 Solving -400 + 890i + -5ix + -400i2 + 8i2x = 0 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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