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Simplifying 3x + 27i = -18 + -3yi Reorder the terms: 27i + 3x = -18 + -3yi Solving 27i + 3x = -18 + -3iy Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '3iy' to each side of the equation. 27i + 3iy + 3x = -18 + -3iy + 3iy Combine like terms: -3iy + 3iy = 0 27i + 3iy + 3x = -18 + 0 27i + 3iy + 3x = -18 Add '-3x' to each side of the equation. 27i + 3iy + 3x + -3x = -18 + -3x Combine like terms: 3x + -3x = 0 27i + 3iy + 0 = -18 + -3x 27i + 3iy = -18 + -3x Reorder the terms: 18 + 27i + 3iy + 3x = -18 + -3x + 18 + 3x Reorder the terms: 18 + 27i + 3iy + 3x = -18 + 18 + -3x + 3x Combine like terms: -18 + 18 = 0 18 + 27i + 3iy + 3x = 0 + -3x + 3x 18 + 27i + 3iy + 3x = -3x + 3x Combine like terms: -3x + 3x = 0 18 + 27i + 3iy + 3x = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(6 + 9i + iy + x) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + 9i + iy + x)' equal to zero and attempt to solve: Simplifying 6 + 9i + iy + x = 0 Solving 6 + 9i + iy + x = 0 Move all terms containing i to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + 9i + iy + -6 + x = 0 + -6 Reorder the terms: 6 + -6 + 9i + iy + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 9i + iy + x = 0 + -6 9i + iy + x = 0 + -6 Combine like terms: 0 + -6 = -6 9i + iy + x = -6 Add '-1x' to each side of the equation. 9i + iy + x + -1x = -6 + -1x Combine like terms: x + -1x = 0 9i + iy + 0 = -6 + -1x 9i + iy = -6 + -1x 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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