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Simplifying 4(x + -1(3 + -1i))(x + -1(3 + i))(x2 + 16i) = 0 4(x + (3 * -1 + -1i * -1))(x + -1(3 + i))(x2 + 16i) = 0 4(x + (-3 + 1i))(x + -1(3 + i))(x2 + 16i) = 0 Reorder the terms: 4(-3 + 1i + x)(x + -1(3 + i))(x2 + 16i) = 0 4(-3 + 1i + x)(x + (3 * -1 + i * -1))(x2 + 16i) = 0 4(-3 + 1i + x)(x + (-3 + -1i))(x2 + 16i) = 0 Reorder the terms: 4(-3 + 1i + x)(-3 + -1i + x)(x2 + 16i) = 0 Reorder the terms: 4(-3 + 1i + x)(-3 + -1i + x)(16i + x2) = 0 Multiply (-3 + 1i + x) * (-3 + -1i + x) 4(-3(-3 + -1i + x) + 1i * (-3 + -1i + x) + x(-3 + -1i + x))(16i + x2) = 0 4((-3 * -3 + -1i * -3 + x * -3) + 1i * (-3 + -1i + x) + x(-3 + -1i + x))(16i + x2) = 0 4((9 + 3i + -3x) + 1i * (-3 + -1i + x) + x(-3 + -1i + x))(16i + x2) = 0 4(9 + 3i + -3x + (-3 * 1i + -1i * 1i + x * 1i) + x(-3 + -1i + x))(16i + x2) = 0 Reorder the terms: 4(9 + 3i + -3x + (-3i + 1ix + -1i2) + x(-3 + -1i + x))(16i + x2) = 0 4(9 + 3i + -3x + (-3i + 1ix + -1i2) + x(-3 + -1i + x))(16i + x2) = 0 4(9 + 3i + -3x + -3i + 1ix + -1i2 + (-3 * x + -1i * x + x * x))(16i + x2) = 0 Reorder the terms: 4(9 + 3i + -3x + -3i + 1ix + -1i2 + (-1ix + -3x + x2))(16i + x2) = 0 4(9 + 3i + -3x + -3i + 1ix + -1i2 + (-1ix + -3x + x2))(16i + x2) = 0 Reorder the terms: 4(9 + 3i + -3i + 1ix + -1ix + -1i2 + -3x + -3x + x2)(16i + x2) = 0 Combine like terms: 3i + -3i = 0 4(9 + 0 + 1ix + -1ix + -1i2 + -3x + -3x + x2)(16i + x2) = 0 4(9 + 1ix + -1ix + -1i2 + -3x + -3x + x2)(16i + x2) = 0 Combine like terms: 1ix + -1ix = 0 4(9 + 0 + -1i2 + -3x + -3x + x2)(16i + x2) = 0 4(9 + -1i2 + -3x + -3x + x2)(16i + x2) = 0 Combine like terms: -3x + -3x = -6x 4(9 + -1i2 + -6x + x2)(16i + x2) = 0 Multiply (9 + -1i2 + -6x + x2) * (16i + x2) 4(9(16i + x2) + -1i2 * (16i + x2) + -6x * (16i + x2) + x2(16i + x2)) = 0 4((16i * 9 + x2 * 9) + -1i2 * (16i + x2) + -6x * (16i + x2) + x2(16i + x2)) = 0 4((144i + 9x2) + -1i2 * (16i + x2) + -6x * (16i + x2) + x2(16i + x2)) = 0 4(144i + 9x2 + (16i * -1i2 + x2 * -1i2) + -6x * (16i + x2) + x2(16i + x2)) = 0 Reorder the terms: 4(144i + 9x2 + (-1i2x2 + -16i3) + -6x * (16i + x2) + x2(16i + x2)) = 0 4(144i + 9x2 + (-1i2x2 + -16i3) + -6x * (16i + x2) + x2(16i + x2)) = 0 4(144i + 9x2 + -1i2x2 + -16i3 + (16i * -6x + x2 * -6x) + x2(16i + x2)) = 0 4(144i + 9x2 + -1i2x2 + -16i3 + (-96ix + -6x3) + x2(16i + x2)) = 0 4(144i + 9x2 + -1i2x2 + -16i3 + -96ix + -6x3 + (16i * x2 + x2 * x2)) = 0 4(144i + 9x2 + -1i2x2 + -16i3 + -96ix + -6x3 + (16ix2 + x4)) = 0 Reorder the terms: 4(144i + -96ix + 16ix2 + -1i2x2 + -16i3 + 9x2 + -6x3 + x4) = 0 4(144i + -96ix + 16ix2 + -1i2x2 + -16i3 + 9x2 + -6x3 + x4) = 0 (144i * 4 + -96ix * 4 + 16ix2 * 4 + -1i2x2 * 4 + -16i3 * 4 + 9x2 * 4 + -6x3 * 4 + x4 * 4) = 0 (576i + -384ix + 64ix2 + -4i2x2 + -64i3 + 36x2 + -24x3 + 4x4) = 0 Solving 576i + -384ix + 64ix2 + -4i2x2 + -64i3 + 36x2 + -24x3 + 4x4 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(144i + -96ix + 16ix2 + -1i2x2 + -16i3 + 9x2 + -6x3 + x4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(144i + -96ix + 16ix2 + -1i2x2 + -16i3 + 9x2 + -6x3 + x4)' equal to zero and attempt to solve: Simplifying 144i + -96ix + 16ix2 + -1i2x2 + -16i3 + 9x2 + -6x3 + x4 = 0 Solving 144i + -96ix + 16ix2 + -1i2x2 + -16i3 + 9x2 + -6x3 + x4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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