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Simplifying 0 = [x + -1(5 + 3i)][x + -1(5 + -3i)] 0 = [x + (5 * -1 + 3i * -1)][x + -1(5 + -3i)] 0 = [x + (-5 + -3i)][x + -1(5 + -3i)] Reorder the terms: 0 = [-5 + -3i + x][x + -1(5 + -3i)] 0 = [-5 + -3i + x][x + (5 * -1 + -3i * -1)] 0 = [-5 + -3i + x][x + (-5 + 3i)] Reorder the terms: 0 = [-5 + -3i + x][-5 + 3i + x] Multiply [-5 + -3i + x] * [-5 + 3i + x] 0 = [-5[-5 + 3i + x] + -3i * [-5 + 3i + x] + x[-5 + 3i + x]] 0 = [[-5 * -5 + 3i * -5 + x * -5] + -3i * [-5 + 3i + x] + x[-5 + 3i + x]] 0 = [[25 + -15i + -5x] + -3i * [-5 + 3i + x] + x[-5 + 3i + x]] 0 = [25 + -15i + -5x + [-5 * -3i + 3i * -3i + x * -3i] + x[-5 + 3i + x]] Reorder the terms: 0 = [25 + -15i + -5x + [15i + -3ix + -9i2] + x[-5 + 3i + x]] 0 = [25 + -15i + -5x + [15i + -3ix + -9i2] + x[-5 + 3i + x]] 0 = [25 + -15i + -5x + 15i + -3ix + -9i2 + [-5 * x + 3i * x + x * x]] Reorder the terms: 0 = [25 + -15i + -5x + 15i + -3ix + -9i2 + [3ix + -5x + x2]] 0 = [25 + -15i + -5x + 15i + -3ix + -9i2 + [3ix + -5x + x2]] Reorder the terms: 0 = [25 + -15i + 15i + -3ix + 3ix + -9i2 + -5x + -5x + x2] Combine like terms: -15i + 15i = 0 0 = [25 + 0 + -3ix + 3ix + -9i2 + -5x + -5x + x2] 0 = [25 + -3ix + 3ix + -9i2 + -5x + -5x + x2] Combine like terms: -3ix + 3ix = 0 0 = [25 + 0 + -9i2 + -5x + -5x + x2] 0 = [25 + -9i2 + -5x + -5x + x2] Combine like terms: -5x + -5x = -10x 0 = [25 + -9i2 + -10x + x2] Solving 0 = 25 + -9i2 + -10x + x2 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '9i2' to each side of the equation. 0 + 9i2 = 25 + -9i2 + -10x + 9i2 + x2 Remove the zero: 9i2 = 25 + -9i2 + -10x + 9i2 + x2 Reorder the terms: 9i2 = 25 + -9i2 + 9i2 + -10x + x2 Combine like terms: -9i2 + 9i2 = 0 9i2 = 25 + 0 + -10x + x2 9i2 = 25 + -10x + x2 Divide each side by '9'. i2 = 2.777777778 + -1.111111111x + 0.1111111111x2 Simplifying i2 = 2.777777778 + -1.111111111x + 0.1111111111x2 Reorder the terms: -2.777777778 + i2 + 1.111111111x + -0.1111111111x2 = 2.777777778 + -1.111111111x + 0.1111111111x2 + -2.777777778 + 1.111111111x + -0.1111111111x2 Reorder the terms: -2.777777778 + i2 + 1.111111111x + -0.1111111111x2 = 2.777777778 + -2.777777778 + -1.111111111x + 1.111111111x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: 2.777777778 + -2.777777778 = 0.000000000 -2.777777778 + i2 + 1.111111111x + -0.1111111111x2 = 0.000000000 + -1.111111111x + 1.111111111x + 0.1111111111x2 + -0.1111111111x2 -2.777777778 + i2 + 1.111111111x + -0.1111111111x2 = -1.111111111x + 1.111111111x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: -1.111111111x + 1.111111111x = 0.000000000 -2.777777778 + i2 + 1.111111111x + -0.1111111111x2 = 0.000000000 + 0.1111111111x2 + -0.1111111111x2 -2.777777778 + i2 + 1.111111111x + -0.1111111111x2 = 0.1111111111x2 + -0.1111111111x2 Combine like terms: 0.1111111111x2 + -0.1111111111x2 = 0.0000000000 -2.777777778 + i2 + 1.111111111x + -0.1111111111x2 = 0.0000000000 The solution to this equation could not be determined.
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