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Simplifying 3(8 + 5i) + -1i(6 + -1i) = 0 (8 * 3 + 5i * 3) + -1i(6 + -1i) = 0 (24 + 15i) + -1i(6 + -1i) = 0 24 + 15i + (6 * -1i + -1i * -1i) = 0 24 + 15i + (-6i + 1i2) = 0 Combine like terms: 15i + -6i = 9i 24 + 9i + 1i2 = 0 Solving 24 + 9i + 1i2 = 0 Solving for variable 'i'. Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 9i + -24 + i2 = 0 + -24 Reorder the terms: 24 + -24 + 9i + i2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 9i + i2 = 0 + -24 9i + i2 = 0 + -24 Combine like terms: 0 + -24 = -24 9i + i2 = -24 The i term is 9i. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9i + 20.25 + i2 = -24 + 20.25 Reorder the terms: 20.25 + 9i + i2 = -24 + 20.25 Combine like terms: -24 + 20.25 = -3.75 20.25 + 9i + i2 = -3.75 Factor a perfect square on the left side: (i + 4.5)(i + 4.5) = -3.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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