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Simplifying 4x + (x + 3i)(x + -3i) + -5x + 7 = 0 Reorder the terms: 4x + (3i + x)(x + -3i) + -5x + 7 = 0 Reorder the terms: 4x + (3i + x)(-3i + x) + -5x + 7 = 0 Multiply (3i + x) * (-3i + x) 4x + (3i * (-3i + x) + x(-3i + x)) + -5x + 7 = 0 4x + ((-3i * 3i + x * 3i) + x(-3i + x)) + -5x + 7 = 0 Reorder the terms: 4x + ((3ix + -9i2) + x(-3i + x)) + -5x + 7 = 0 4x + ((3ix + -9i2) + x(-3i + x)) + -5x + 7 = 0 4x + (3ix + -9i2 + (-3i * x + x * x)) + -5x + 7 = 0 4x + (3ix + -9i2 + (-3ix + x2)) + -5x + 7 = 0 Reorder the terms: 4x + (3ix + -3ix + -9i2 + x2) + -5x + 7 = 0 Combine like terms: 3ix + -3ix = 0 4x + (0 + -9i2 + x2) + -5x + 7 = 0 4x + (-9i2 + x2) + -5x + 7 = 0 Reorder the terms: 7 + -9i2 + 4x + -5x + x2 = 0 Combine like terms: 4x + -5x = -1x 7 + -9i2 + -1x + x2 = 0 Solving 7 + -9i2 + -1x + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -9i2 + -1x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -9i2 + -1x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -9i2 + -1x + x2 = 0 + -7 -9i2 + -1x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -9i2 + -1x + x2 = -7 Add 'x' to each side of the equation. -9i2 + -1x + x + x2 = -7 + x Combine like terms: -1x + x = 0 -9i2 + 0 + x2 = -7 + x -9i2 + x2 = -7 + x Add '-1x2' to each side of the equation. -9i2 + x2 + -1x2 = -7 + x + -1x2 Combine like terms: x2 + -1x2 = 0 -9i2 + 0 = -7 + x + -1x2 -9i2 = -7 + x + -1x2 Divide each side by '-9'. i2 = 0.7777777778 + -0.1111111111x + 0.1111111111x2 Simplifying i2 = 0.7777777778 + -0.1111111111x + 0.1111111111x2 Reorder the terms: -0.7777777778 + i2 + 0.1111111111x + -0.1111111111x2 = 0.7777777778 + -0.1111111111x + 0.1111111111x2 + -0.7777777778 + 0.1111111111x + -0.1111111111x2 Reorder the terms: -0.7777777778 + i2 + 0.1111111111x + -0.1111111111x2 = 0.7777777778 + -0.7777777778 + -0.1111111111x + 0.1111111111x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 -0.7777777778 + i2 + 0.1111111111x + -0.1111111111x2 = 0.0000000000 + -0.1111111111x + 0.1111111111x + 0.1111111111x2 + -0.1111111111x2 -0.7777777778 + i2 + 0.1111111111x + -0.1111111111x2 = -0.1111111111x + 0.1111111111x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: -0.1111111111x + 0.1111111111x = 0.0000000000 -0.7777777778 + i2 + 0.1111111111x + -0.1111111111x2 = 0.0000000000 + 0.1111111111x2 + -0.1111111111x2 -0.7777777778 + i2 + 0.1111111111x + -0.1111111111x2 = 0.1111111111x2 + -0.1111111111x2 Combine like terms: 0.1111111111x2 + -0.1111111111x2 = 0.0000000000 -0.7777777778 + i2 + 0.1111111111x + -0.1111111111x2 = 0.0000000000 The solution to this equation could not be determined.
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