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Simplifying [x + -1(4 + 5i)][x + -1(4 + -5i)] = 0 [x + (4 * -1 + 5i * -1)][x + -1(4 + -5i)] = 0 [x + (-4 + -5i)][x + -1(4 + -5i)] = 0 Reorder the terms: [-4 + -5i + x][x + -1(4 + -5i)] = 0 [-4 + -5i + x][x + (4 * -1 + -5i * -1)] = 0 [-4 + -5i + x][x + (-4 + 5i)] = 0 Reorder the terms: [-4 + -5i + x][-4 + 5i + x] = 0 Multiply [-4 + -5i + x] * [-4 + 5i + x] [-4[-4 + 5i + x] + -5i * [-4 + 5i + x] + x[-4 + 5i + x]] = 0 [[-4 * -4 + 5i * -4 + x * -4] + -5i * [-4 + 5i + x] + x[-4 + 5i + x]] = 0 [[16 + -20i + -4x] + -5i * [-4 + 5i + x] + x[-4 + 5i + x]] = 0 [16 + -20i + -4x + [-4 * -5i + 5i * -5i + x * -5i] + x[-4 + 5i + x]] = 0 Reorder the terms: [16 + -20i + -4x + [20i + -5ix + -25i2] + x[-4 + 5i + x]] = 0 [16 + -20i + -4x + [20i + -5ix + -25i2] + x[-4 + 5i + x]] = 0 [16 + -20i + -4x + 20i + -5ix + -25i2 + [-4 * x + 5i * x + x * x]] = 0 Reorder the terms: [16 + -20i + -4x + 20i + -5ix + -25i2 + [5ix + -4x + x2]] = 0 [16 + -20i + -4x + 20i + -5ix + -25i2 + [5ix + -4x + x2]] = 0 Reorder the terms: [16 + -20i + 20i + -5ix + 5ix + -25i2 + -4x + -4x + x2] = 0 Combine like terms: -20i + 20i = 0 [16 + 0 + -5ix + 5ix + -25i2 + -4x + -4x + x2] = 0 [16 + -5ix + 5ix + -25i2 + -4x + -4x + x2] = 0 Combine like terms: -5ix + 5ix = 0 [16 + 0 + -25i2 + -4x + -4x + x2] = 0 [16 + -25i2 + -4x + -4x + x2] = 0 Combine like terms: -4x + -4x = -8x [16 + -25i2 + -8x + x2] = 0 Solving 16 + -25i2 + -8x + x2 = 0 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 + -25i2 + -8x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -25i2 + -8x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -25i2 + -8x + x2 = 0 + -16 -25i2 + -8x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -25i2 + -8x + x2 = -16 Add '8x' to each side of the equation. -25i2 + -8x + 8x + x2 = -16 + 8x Combine like terms: -8x + 8x = 0 -25i2 + 0 + x2 = -16 + 8x -25i2 + x2 = -16 + 8x Add '-1x2' to each side of the equation. -25i2 + x2 + -1x2 = -16 + 8x + -1x2 Combine like terms: x2 + -1x2 = 0 -25i2 + 0 = -16 + 8x + -1x2 -25i2 = -16 + 8x + -1x2 Divide each side by '-25'. i2 = 0.64 + -0.32x + 0.04x2 Simplifying i2 = 0.64 + -0.32x + 0.04x2 Reorder the terms: -0.64 + i2 + 0.32x + -0.04x2 = 0.64 + -0.32x + 0.04x2 + -0.64 + 0.32x + -0.04x2 Reorder the terms: -0.64 + i2 + 0.32x + -0.04x2 = 0.64 + -0.64 + -0.32x + 0.32x + 0.04x2 + -0.04x2 Combine like terms: 0.64 + -0.64 = 0.00 -0.64 + i2 + 0.32x + -0.04x2 = 0.00 + -0.32x + 0.32x + 0.04x2 + -0.04x2 -0.64 + i2 + 0.32x + -0.04x2 = -0.32x + 0.32x + 0.04x2 + -0.04x2 Combine like terms: -0.32x + 0.32x = 0.00 -0.64 + i2 + 0.32x + -0.04x2 = 0.00 + 0.04x2 + -0.04x2 -0.64 + i2 + 0.32x + -0.04x2 = 0.04x2 + -0.04x2 Combine like terms: 0.04x2 + -0.04x2 = 0.00 -0.64 + i2 + 0.32x + -0.04x2 = 0.00 The solution to this equation could not be determined.
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