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Simplifying [x + -1(2 + -6i)][x + -1(2 + 6i)] = 0 [x + (2 * -1 + -6i * -1)][x + -1(2 + 6i)] = 0 [x + (-2 + 6i)][x + -1(2 + 6i)] = 0 Reorder the terms: [-2 + 6i + x][x + -1(2 + 6i)] = 0 [-2 + 6i + x][x + (2 * -1 + 6i * -1)] = 0 [-2 + 6i + x][x + (-2 + -6i)] = 0 Reorder the terms: [-2 + 6i + x][-2 + -6i + x] = 0 Multiply [-2 + 6i + x] * [-2 + -6i + x] [-2[-2 + -6i + x] + 6i * [-2 + -6i + x] + x[-2 + -6i + x]] = 0 [[-2 * -2 + -6i * -2 + x * -2] + 6i * [-2 + -6i + x] + x[-2 + -6i + x]] = 0 [[4 + 12i + -2x] + 6i * [-2 + -6i + x] + x[-2 + -6i + x]] = 0 [4 + 12i + -2x + [-2 * 6i + -6i * 6i + x * 6i] + x[-2 + -6i + x]] = 0 Reorder the terms: [4 + 12i + -2x + [-12i + 6ix + -36i2] + x[-2 + -6i + x]] = 0 [4 + 12i + -2x + [-12i + 6ix + -36i2] + x[-2 + -6i + x]] = 0 [4 + 12i + -2x + -12i + 6ix + -36i2 + [-2 * x + -6i * x + x * x]] = 0 Reorder the terms: [4 + 12i + -2x + -12i + 6ix + -36i2 + [-6ix + -2x + x2]] = 0 [4 + 12i + -2x + -12i + 6ix + -36i2 + [-6ix + -2x + x2]] = 0 Reorder the terms: [4 + 12i + -12i + 6ix + -6ix + -36i2 + -2x + -2x + x2] = 0 Combine like terms: 12i + -12i = 0 [4 + 0 + 6ix + -6ix + -36i2 + -2x + -2x + x2] = 0 [4 + 6ix + -6ix + -36i2 + -2x + -2x + x2] = 0 Combine like terms: 6ix + -6ix = 0 [4 + 0 + -36i2 + -2x + -2x + x2] = 0 [4 + -36i2 + -2x + -2x + x2] = 0 Combine like terms: -2x + -2x = -4x [4 + -36i2 + -4x + x2] = 0 Solving 4 + -36i2 + -4x + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -36i2 + -4x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -36i2 + -4x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -36i2 + -4x + x2 = 0 + -4 -36i2 + -4x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -36i2 + -4x + x2 = -4 Add '4x' to each side of the equation. -36i2 + -4x + 4x + x2 = -4 + 4x Combine like terms: -4x + 4x = 0 -36i2 + 0 + x2 = -4 + 4x -36i2 + x2 = -4 + 4x Add '-1x2' to each side of the equation. -36i2 + x2 + -1x2 = -4 + 4x + -1x2 Combine like terms: x2 + -1x2 = 0 -36i2 + 0 = -4 + 4x + -1x2 -36i2 = -4 + 4x + -1x2 Divide each side by '-36'. i2 = 0.1111111111 + -0.1111111111x + 0.02777777778x2 Simplifying i2 = 0.1111111111 + -0.1111111111x + 0.02777777778x2 Reorder the terms: -0.1111111111 + i2 + 0.1111111111x + -0.02777777778x2 = 0.1111111111 + -0.1111111111x + 0.02777777778x2 + -0.1111111111 + 0.1111111111x + -0.02777777778x2 Reorder the terms: -0.1111111111 + i2 + 0.1111111111x + -0.02777777778x2 = 0.1111111111 + -0.1111111111 + -0.1111111111x + 0.1111111111x + 0.02777777778x2 + -0.02777777778x2 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 -0.1111111111 + i2 + 0.1111111111x + -0.02777777778x2 = 0.0000000000 + -0.1111111111x + 0.1111111111x + 0.02777777778x2 + -0.02777777778x2 -0.1111111111 + i2 + 0.1111111111x + -0.02777777778x2 = -0.1111111111x + 0.1111111111x + 0.02777777778x2 + -0.02777777778x2 Combine like terms: -0.1111111111x + 0.1111111111x = 0.0000000000 -0.1111111111 + i2 + 0.1111111111x + -0.02777777778x2 = 0.0000000000 + 0.02777777778x2 + -0.02777777778x2 -0.1111111111 + i2 + 0.1111111111x + -0.02777777778x2 = 0.02777777778x2 + -0.02777777778x2 Combine like terms: 0.02777777778x2 + -0.02777777778x2 = 0.00000000000 -0.1111111111 + i2 + 0.1111111111x + -0.02777777778x2 = 0.00000000000 The solution to this equation could not be determined.
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