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Simplifying [x + -1(6 + 5i)][x + -1(6 + -5i)] = 0 [x + (6 * -1 + 5i * -1)][x + -1(6 + -5i)] = 0 [x + (-6 + -5i)][x + -1(6 + -5i)] = 0 Reorder the terms: [-6 + -5i + x][x + -1(6 + -5i)] = 0 [-6 + -5i + x][x + (6 * -1 + -5i * -1)] = 0 [-6 + -5i + x][x + (-6 + 5i)] = 0 Reorder the terms: [-6 + -5i + x][-6 + 5i + x] = 0 Multiply [-6 + -5i + x] * [-6 + 5i + x] [-6[-6 + 5i + x] + -5i * [-6 + 5i + x] + x[-6 + 5i + x]] = 0 [[-6 * -6 + 5i * -6 + x * -6] + -5i * [-6 + 5i + x] + x[-6 + 5i + x]] = 0 [[36 + -30i + -6x] + -5i * [-6 + 5i + x] + x[-6 + 5i + x]] = 0 [36 + -30i + -6x + [-6 * -5i + 5i * -5i + x * -5i] + x[-6 + 5i + x]] = 0 Reorder the terms: [36 + -30i + -6x + [30i + -5ix + -25i2] + x[-6 + 5i + x]] = 0 [36 + -30i + -6x + [30i + -5ix + -25i2] + x[-6 + 5i + x]] = 0 [36 + -30i + -6x + 30i + -5ix + -25i2 + [-6 * x + 5i * x + x * x]] = 0 Reorder the terms: [36 + -30i + -6x + 30i + -5ix + -25i2 + [5ix + -6x + x2]] = 0 [36 + -30i + -6x + 30i + -5ix + -25i2 + [5ix + -6x + x2]] = 0 Reorder the terms: [36 + -30i + 30i + -5ix + 5ix + -25i2 + -6x + -6x + x2] = 0 Combine like terms: -30i + 30i = 0 [36 + 0 + -5ix + 5ix + -25i2 + -6x + -6x + x2] = 0 [36 + -5ix + 5ix + -25i2 + -6x + -6x + x2] = 0 Combine like terms: -5ix + 5ix = 0 [36 + 0 + -25i2 + -6x + -6x + x2] = 0 [36 + -25i2 + -6x + -6x + x2] = 0 Combine like terms: -6x + -6x = -12x [36 + -25i2 + -12x + x2] = 0 Solving 36 + -25i2 + -12x + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -25i2 + -12x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -25i2 + -12x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -25i2 + -12x + x2 = 0 + -36 -25i2 + -12x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -25i2 + -12x + x2 = -36 Add '12x' to each side of the equation. -25i2 + -12x + 12x + x2 = -36 + 12x Combine like terms: -12x + 12x = 0 -25i2 + 0 + x2 = -36 + 12x -25i2 + x2 = -36 + 12x Add '-1x2' to each side of the equation. -25i2 + x2 + -1x2 = -36 + 12x + -1x2 Combine like terms: x2 + -1x2 = 0 -25i2 + 0 = -36 + 12x + -1x2 -25i2 = -36 + 12x + -1x2 Divide each side by '-25'. i2 = 1.44 + -0.48x + 0.04x2 Simplifying i2 = 1.44 + -0.48x + 0.04x2 Reorder the terms: -1.44 + i2 + 0.48x + -0.04x2 = 1.44 + -0.48x + 0.04x2 + -1.44 + 0.48x + -0.04x2 Reorder the terms: -1.44 + i2 + 0.48x + -0.04x2 = 1.44 + -1.44 + -0.48x + 0.48x + 0.04x2 + -0.04x2 Combine like terms: 1.44 + -1.44 = 0.00 -1.44 + i2 + 0.48x + -0.04x2 = 0.00 + -0.48x + 0.48x + 0.04x2 + -0.04x2 -1.44 + i2 + 0.48x + -0.04x2 = -0.48x + 0.48x + 0.04x2 + -0.04x2 Combine like terms: -0.48x + 0.48x = 0.00 -1.44 + i2 + 0.48x + -0.04x2 = 0.00 + 0.04x2 + -0.04x2 -1.44 + i2 + 0.48x + -0.04x2 = 0.04x2 + -0.04x2 Combine like terms: 0.04x2 + -0.04x2 = 0.00 -1.44 + i2 + 0.48x + -0.04x2 = 0.00 The solution to this equation could not be determined.
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