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Simplifying (-5 + -1i)(x) = 3 + 11i Reorder the terms for easier multiplication: x(-5 + -1i) = 3 + 11i (-5 * x + -1i * x) = 3 + 11i Reorder the terms: (-1ix + -5x) = 3 + 11i (-1ix + -5x) = 3 + 11i Solving -1ix + -5x = 3 + 11i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-11i' to each side of the equation. -1ix + -11i + -5x = 3 + 11i + -11i Reorder the terms: -11i + -1ix + -5x = 3 + 11i + -11i Combine like terms: 11i + -11i = 0 -11i + -1ix + -5x = 3 + 0 -11i + -1ix + -5x = 3 Add '5x' to each side of the equation. -11i + -1ix + -5x + 5x = 3 + 5x Combine like terms: -5x + 5x = 0 -11i + -1ix + 0 = 3 + 5x -11i + -1ix = 3 + 5x Reorder the terms: -3 + -11i + -1ix + -5x = 3 + 5x + -3 + -5x Reorder the terms: -3 + -11i + -1ix + -5x = 3 + -3 + 5x + -5x Combine like terms: 3 + -3 = 0 -3 + -11i + -1ix + -5x = 0 + 5x + -5x -3 + -11i + -1ix + -5x = 5x + -5x Combine like terms: 5x + -5x = 0 -3 + -11i + -1ix + -5x = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 11i + ix + 5x) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 11i + ix + 5x)' equal to zero and attempt to solve: Simplifying 3 + 11i + ix + 5x = 0 Solving 3 + 11i + ix + 5x = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + 11i + ix + -3 + 5x = 0 + -3 Reorder the terms: 3 + -3 + 11i + ix + 5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 11i + ix + 5x = 0 + -3 11i + ix + 5x = 0 + -3 Combine like terms: 0 + -3 = -3 11i + ix + 5x = -3 Add '-5x' to each side of the equation. 11i + ix + 5x + -5x = -3 + -5x Combine like terms: 5x + -5x = 0 11i + ix + 0 = -3 + -5x 11i + ix = -3 + -5x 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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