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Simplifying [x + -1(2 + 9i)][x + -1(2 + -9i)] = 0 [x + (2 * -1 + 9i * -1)][x + -1(2 + -9i)] = 0 [x + (-2 + -9i)][x + -1(2 + -9i)] = 0 Reorder the terms: [-2 + -9i + x][x + -1(2 + -9i)] = 0 [-2 + -9i + x][x + (2 * -1 + -9i * -1)] = 0 [-2 + -9i + x][x + (-2 + 9i)] = 0 Reorder the terms: [-2 + -9i + x][-2 + 9i + x] = 0 Multiply [-2 + -9i + x] * [-2 + 9i + x] [-2[-2 + 9i + x] + -9i * [-2 + 9i + x] + x[-2 + 9i + x]] = 0 [[-2 * -2 + 9i * -2 + x * -2] + -9i * [-2 + 9i + x] + x[-2 + 9i + x]] = 0 [[4 + -18i + -2x] + -9i * [-2 + 9i + x] + x[-2 + 9i + x]] = 0 [4 + -18i + -2x + [-2 * -9i + 9i * -9i + x * -9i] + x[-2 + 9i + x]] = 0 Reorder the terms: [4 + -18i + -2x + [18i + -9ix + -81i2] + x[-2 + 9i + x]] = 0 [4 + -18i + -2x + [18i + -9ix + -81i2] + x[-2 + 9i + x]] = 0 [4 + -18i + -2x + 18i + -9ix + -81i2 + [-2 * x + 9i * x + x * x]] = 0 Reorder the terms: [4 + -18i + -2x + 18i + -9ix + -81i2 + [9ix + -2x + x2]] = 0 [4 + -18i + -2x + 18i + -9ix + -81i2 + [9ix + -2x + x2]] = 0 Reorder the terms: [4 + -18i + 18i + -9ix + 9ix + -81i2 + -2x + -2x + x2] = 0 Combine like terms: -18i + 18i = 0 [4 + 0 + -9ix + 9ix + -81i2 + -2x + -2x + x2] = 0 [4 + -9ix + 9ix + -81i2 + -2x + -2x + x2] = 0 Combine like terms: -9ix + 9ix = 0 [4 + 0 + -81i2 + -2x + -2x + x2] = 0 [4 + -81i2 + -2x + -2x + x2] = 0 Combine like terms: -2x + -2x = -4x [4 + -81i2 + -4x + x2] = 0 Solving 4 + -81i2 + -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 + -81i2 + -4x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -81i2 + -4x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -81i2 + -4x + x2 = 0 + -4 -81i2 + -4x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -81i2 + -4x + x2 = -4 Add '4x' to each side of the equation. -81i2 + -4x + 4x + x2 = -4 + 4x Combine like terms: -4x + 4x = 0 -81i2 + 0 + x2 = -4 + 4x -81i2 + x2 = -4 + 4x Add '-1x2' to each side of the equation. -81i2 + x2 + -1x2 = -4 + 4x + -1x2 Combine like terms: x2 + -1x2 = 0 -81i2 + 0 = -4 + 4x + -1x2 -81i2 = -4 + 4x + -1x2 Divide each side by '-81'. i2 = 0.04938271605 + -0.04938271605x + 0.01234567901x2 Simplifying i2 = 0.04938271605 + -0.04938271605x + 0.01234567901x2 Reorder the terms: -0.04938271605 + i2 + 0.04938271605x + -0.01234567901x2 = 0.04938271605 + -0.04938271605x + 0.01234567901x2 + -0.04938271605 + 0.04938271605x + -0.01234567901x2 Reorder the terms: -0.04938271605 + i2 + 0.04938271605x + -0.01234567901x2 = 0.04938271605 + -0.04938271605 + -0.04938271605x + 0.04938271605x + 0.01234567901x2 + -0.01234567901x2 Combine like terms: 0.04938271605 + -0.04938271605 = 0.00000000000 -0.04938271605 + i2 + 0.04938271605x + -0.01234567901x2 = 0.00000000000 + -0.04938271605x + 0.04938271605x + 0.01234567901x2 + -0.01234567901x2 -0.04938271605 + i2 + 0.04938271605x + -0.01234567901x2 = -0.04938271605x + 0.04938271605x + 0.01234567901x2 + -0.01234567901x2 Combine like terms: -0.04938271605x + 0.04938271605x = 0.00000000000 -0.04938271605 + i2 + 0.04938271605x + -0.01234567901x2 = 0.00000000000 + 0.01234567901x2 + -0.01234567901x2 -0.04938271605 + i2 + 0.04938271605x + -0.01234567901x2 = 0.01234567901x2 + -0.01234567901x2 Combine like terms: 0.01234567901x2 + -0.01234567901x2 = 0.00000000000 -0.04938271605 + i2 + 0.04938271605x + -0.01234567901x2 = 0.00000000000 The solution to this equation could not be determined.
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