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Simplifying [x + -1(5 + -6i)][x + -1(5 + 6i)] = 0 [x + (5 * -1 + -6i * -1)][x + -1(5 + 6i)] = 0 [x + (-5 + 6i)][x + -1(5 + 6i)] = 0 Reorder the terms: [-5 + 6i + x][x + -1(5 + 6i)] = 0 [-5 + 6i + x][x + (5 * -1 + 6i * -1)] = 0 [-5 + 6i + x][x + (-5 + -6i)] = 0 Reorder the terms: [-5 + 6i + x][-5 + -6i + x] = 0 Multiply [-5 + 6i + x] * [-5 + -6i + x] [-5[-5 + -6i + x] + 6i * [-5 + -6i + x] + x[-5 + -6i + x]] = 0 [[-5 * -5 + -6i * -5 + x * -5] + 6i * [-5 + -6i + x] + x[-5 + -6i + x]] = 0 [[25 + 30i + -5x] + 6i * [-5 + -6i + x] + x[-5 + -6i + x]] = 0 [25 + 30i + -5x + [-5 * 6i + -6i * 6i + x * 6i] + x[-5 + -6i + x]] = 0 Reorder the terms: [25 + 30i + -5x + [-30i + 6ix + -36i2] + x[-5 + -6i + x]] = 0 [25 + 30i + -5x + [-30i + 6ix + -36i2] + x[-5 + -6i + x]] = 0 [25 + 30i + -5x + -30i + 6ix + -36i2 + [-5 * x + -6i * x + x * x]] = 0 Reorder the terms: [25 + 30i + -5x + -30i + 6ix + -36i2 + [-6ix + -5x + x2]] = 0 [25 + 30i + -5x + -30i + 6ix + -36i2 + [-6ix + -5x + x2]] = 0 Reorder the terms: [25 + 30i + -30i + 6ix + -6ix + -36i2 + -5x + -5x + x2] = 0 Combine like terms: 30i + -30i = 0 [25 + 0 + 6ix + -6ix + -36i2 + -5x + -5x + x2] = 0 [25 + 6ix + -6ix + -36i2 + -5x + -5x + x2] = 0 Combine like terms: 6ix + -6ix = 0 [25 + 0 + -36i2 + -5x + -5x + x2] = 0 [25 + -36i2 + -5x + -5x + x2] = 0 Combine like terms: -5x + -5x = -10x [25 + -36i2 + -10x + x2] = 0 Solving 25 + -36i2 + -10x + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -36i2 + -10x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -36i2 + -10x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -36i2 + -10x + x2 = 0 + -25 -36i2 + -10x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -36i2 + -10x + x2 = -25 Add '10x' to each side of the equation. -36i2 + -10x + 10x + x2 = -25 + 10x Combine like terms: -10x + 10x = 0 -36i2 + 0 + x2 = -25 + 10x -36i2 + x2 = -25 + 10x Add '-1x2' to each side of the equation. -36i2 + x2 + -1x2 = -25 + 10x + -1x2 Combine like terms: x2 + -1x2 = 0 -36i2 + 0 = -25 + 10x + -1x2 -36i2 = -25 + 10x + -1x2 Divide each side by '-36'. i2 = 0.6944444444 + -0.2777777778x + 0.02777777778x2 Simplifying i2 = 0.6944444444 + -0.2777777778x + 0.02777777778x2 Reorder the terms: -0.6944444444 + i2 + 0.2777777778x + -0.02777777778x2 = 0.6944444444 + -0.2777777778x + 0.02777777778x2 + -0.6944444444 + 0.2777777778x + -0.02777777778x2 Reorder the terms: -0.6944444444 + i2 + 0.2777777778x + -0.02777777778x2 = 0.6944444444 + -0.6944444444 + -0.2777777778x + 0.2777777778x + 0.02777777778x2 + -0.02777777778x2 Combine like terms: 0.6944444444 + -0.6944444444 = 0.0000000000 -0.6944444444 + i2 + 0.2777777778x + -0.02777777778x2 = 0.0000000000 + -0.2777777778x + 0.2777777778x + 0.02777777778x2 + -0.02777777778x2 -0.6944444444 + i2 + 0.2777777778x + -0.02777777778x2 = -0.2777777778x + 0.2777777778x + 0.02777777778x2 + -0.02777777778x2 Combine like terms: -0.2777777778x + 0.2777777778x = 0.0000000000 -0.6944444444 + i2 + 0.2777777778x + -0.02777777778x2 = 0.0000000000 + 0.02777777778x2 + -0.02777777778x2 -0.6944444444 + i2 + 0.2777777778x + -0.02777777778x2 = 0.02777777778x2 + -0.02777777778x2 Combine like terms: 0.02777777778x2 + -0.02777777778x2 = 0.00000000000 -0.6944444444 + i2 + 0.2777777778x + -0.02777777778x2 = 0.00000000000 The solution to this equation could not be determined.
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