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Simplifying 2(x + -1) + 2yi = -10i + -6 Reorder the terms: 2(-1 + x) + 2yi = -10i + -6 (-1 * 2 + x * 2) + 2yi = -10i + -6 (-2 + 2x) + 2yi = -10i + -6 Reorder the terms: -2 + 2iy + 2x = -10i + -6 Reorder the terms: -2 + 2iy + 2x = -6 + -10i Solving -2 + 2iy + 2x = -6 + -10i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '10i' to each side of the equation. -2 + 2iy + 10i + 2x = -6 + -10i + 10i Reorder the terms: -2 + 10i + 2iy + 2x = -6 + -10i + 10i Combine like terms: -10i + 10i = 0 -2 + 10i + 2iy + 2x = -6 + 0 -2 + 10i + 2iy + 2x = -6 Add '2' to each side of the equation. -2 + 10i + 2iy + 2 + 2x = -6 + 2 Reorder the terms: -2 + 2 + 10i + 2iy + 2x = -6 + 2 Combine like terms: -2 + 2 = 0 0 + 10i + 2iy + 2x = -6 + 2 10i + 2iy + 2x = -6 + 2 Combine like terms: -6 + 2 = -4 10i + 2iy + 2x = -4 Add '-2x' to each side of the equation. 10i + 2iy + 2x + -2x = -4 + -2x Combine like terms: 2x + -2x = 0 10i + 2iy + 0 = -4 + -2x 10i + 2iy = -4 + -2x Reorder the terms: 4 + 10i + 2iy + 2x = -4 + -2x + 4 + 2x Reorder the terms: 4 + 10i + 2iy + 2x = -4 + 4 + -2x + 2x Combine like terms: -4 + 4 = 0 4 + 10i + 2iy + 2x = 0 + -2x + 2x 4 + 10i + 2iy + 2x = -2x + 2x Combine like terms: -2x + 2x = 0 4 + 10i + 2iy + 2x = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 5i + iy + x) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 5i + iy + x)' equal to zero and attempt to solve: Simplifying 2 + 5i + iy + x = 0 Solving 2 + 5i + iy + x = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + 5i + iy + -2 + x = 0 + -2 Reorder the terms: 2 + -2 + 5i + iy + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5i + iy + x = 0 + -2 5i + iy + x = 0 + -2 Combine like terms: 0 + -2 = -2 5i + iy + x = -2 Add '-1x' to each side of the equation. 5i + iy + x + -1x = -2 + -1x Combine like terms: x + -1x = 0 5i + iy + 0 = -2 + -1x 5i + iy = -2 + -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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