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Simplifying 2x + 3i + -1(5 + 2i) = (x + -12i) + (x + -4i) 2x + 3i + (5 * -1 + 2i * -1) = (x + -12i) + (x + -4i) 2x + 3i + (-5 + -2i) = (x + -12i) + (x + -4i) Reorder the terms: -5 + 3i + -2i + 2x = (x + -12i) + (x + -4i) Combine like terms: 3i + -2i = 1i -5 + 1i + 2x = (x + -12i) + (x + -4i) Reorder the terms: -5 + 1i + 2x = (-12i + x) + (x + -4i) Remove parenthesis around (-12i + x) -5 + 1i + 2x = -12i + x + (x + -4i) Reorder the terms: -5 + 1i + 2x = -12i + x + (-4i + x) Remove parenthesis around (-4i + x) -5 + 1i + 2x = -12i + x + -4i + x Reorder the terms: -5 + 1i + 2x = -12i + -4i + x + x Combine like terms: -12i + -4i = -16i -5 + 1i + 2x = -16i + x + x Combine like terms: x + x = 2x -5 + 1i + 2x = -16i + 2x Add '-2x' to each side of the equation. -5 + 1i + 2x + -2x = -16i + 2x + -2x Combine like terms: 2x + -2x = 0 -5 + 1i + 0 = -16i + 2x + -2x -5 + 1i = -16i + 2x + -2x Combine like terms: 2x + -2x = 0 -5 + 1i = -16i + 0 -5 + 1i = -16i Solving -5 + 1i = -16i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '16i' to each side of the equation. -5 + 1i + 16i = -16i + 16i Combine like terms: 1i + 16i = 17i -5 + 17i = -16i + 16i Combine like terms: -16i + 16i = 0 -5 + 17i = 0 Add '5' to each side of the equation. -5 + 5 + 17i = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 17i = 0 + 5 17i = 0 + 5 Combine like terms: 0 + 5 = 5 17i = 5 Divide each side by '17'. i = 0.2941176471 Simplifying i = 0.2941176471
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