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Simplifying 7(2 + -4i) + -1(i)(4 + i) = 0 (2 * 7 + -4i * 7) + -1(i)(4 + i) = 0 (14 + -28i) + -1(i)(4 + i) = 0 14 + -28i + (4 * -1i + i * -1i) = 0 14 + -28i + (-4i + -1i2) = 0 Combine like terms: -28i + -4i = -32i 14 + -32i + -1i2 = 0 Solving 14 + -32i + -1i2 = 0 Solving for variable 'i'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -14 + 32i + i2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 32i + 14 + i2 = 0 + 14 Reorder the terms: -14 + 14 + 32i + i2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 32i + i2 = 0 + 14 32i + i2 = 0 + 14 Combine like terms: 0 + 14 = 14 32i + i2 = 14 The i term is 32i. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32i + 256 + i2 = 14 + 256 Reorder the terms: 256 + 32i + i2 = 14 + 256 Combine like terms: 14 + 256 = 270 256 + 32i + i2 = 270 Factor a perfect square on the left side: (i + 16)(i + 16) = 270 Calculate the square root of the right side: 16.431676725 Break this problem into two subproblems by setting (i + 16) equal to 16.431676725 and -16.431676725.Subproblem 1
i + 16 = 16.431676725 Simplifying i + 16 = 16.431676725 Reorder the terms: 16 + i = 16.431676725 Solving 16 + i = 16.431676725 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + i = 16.431676725 + -16 Combine like terms: 16 + -16 = 0 0 + i = 16.431676725 + -16 i = 16.431676725 + -16 Combine like terms: 16.431676725 + -16 = 0.431676725 i = 0.431676725 Simplifying i = 0.431676725Subproblem 2
i + 16 = -16.431676725 Simplifying i + 16 = -16.431676725 Reorder the terms: 16 + i = -16.431676725 Solving 16 + i = -16.431676725 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + i = -16.431676725 + -16 Combine like terms: 16 + -16 = 0 0 + i = -16.431676725 + -16 i = -16.431676725 + -16 Combine like terms: -16.431676725 + -16 = -32.431676725 i = -32.431676725 Simplifying i = -32.431676725Solution
The solution to the problem is based on the solutions from the subproblems. i = {0.431676725, -32.431676725}
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