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Simplifying 5(x + -4)(x + 4)(x + -5i)(x + 5i) = 0 Reorder the terms: 5(-4 + x)(x + 4)(x + -5i)(x + 5i) = 0 Reorder the terms: 5(-4 + x)(4 + x)(x + -5i)(x + 5i) = 0 Reorder the terms: 5(-4 + x)(4 + x)(-5i + x)(x + 5i) = 0 Reorder the terms: 5(-4 + x)(4 + x)(-5i + x)(5i + x) = 0 Multiply (-4 + x) * (4 + x) 5(-4(4 + x) + x(4 + x))(-5i + x)(5i + x) = 0 5((4 * -4 + x * -4) + x(4 + x))(-5i + x)(5i + x) = 0 5((-16 + -4x) + x(4 + x))(-5i + x)(5i + x) = 0 5(-16 + -4x + (4 * x + x * x))(-5i + x)(5i + x) = 0 5(-16 + -4x + (4x + x2))(-5i + x)(5i + x) = 0 Combine like terms: -4x + 4x = 0 5(-16 + 0 + x2)(-5i + x)(5i + x) = 0 5(-16 + x2)(-5i + x)(5i + x) = 0 Multiply (-16 + x2) * (-5i + x) 5(-16(-5i + x) + x2(-5i + x))(5i + x) = 0 5((-5i * -16 + x * -16) + x2(-5i + x))(5i + x) = 0 5((80i + -16x) + x2(-5i + x))(5i + x) = 0 5(80i + -16x + (-5i * x2 + x * x2))(5i + x) = 0 5(80i + -16x + (-5ix2 + x3))(5i + x) = 0 Reorder the terms: 5(80i + -5ix2 + -16x + x3)(5i + x) = 0 5(80i + -5ix2 + -16x + x3)(5i + x) = 0 Multiply (80i + -5ix2 + -16x + x3) * (5i + x) 5(80i * (5i + x) + -5ix2 * (5i + x) + -16x * (5i + x) + x3(5i + x)) = 0 5((5i * 80i + x * 80i) + -5ix2 * (5i + x) + -16x * (5i + x) + x3(5i + x)) = 0 Reorder the terms: 5((80ix + 400i2) + -5ix2 * (5i + x) + -16x * (5i + x) + x3(5i + x)) = 0 5((80ix + 400i2) + -5ix2 * (5i + x) + -16x * (5i + x) + x3(5i + x)) = 0 5(80ix + 400i2 + (5i * -5ix2 + x * -5ix2) + -16x * (5i + x) + x3(5i + x)) = 0 Reorder the terms: 5(80ix + 400i2 + (-5ix3 + -25i2x2) + -16x * (5i + x) + x3(5i + x)) = 0 5(80ix + 400i2 + (-5ix3 + -25i2x2) + -16x * (5i + x) + x3(5i + x)) = 0 5(80ix + 400i2 + -5ix3 + -25i2x2 + (5i * -16x + x * -16x) + x3(5i + x)) = 0 5(80ix + 400i2 + -5ix3 + -25i2x2 + (-80ix + -16x2) + x3(5i + x)) = 0 5(80ix + 400i2 + -5ix3 + -25i2x2 + -80ix + -16x2 + (5i * x3 + x * x3)) = 0 5(80ix + 400i2 + -5ix3 + -25i2x2 + -80ix + -16x2 + (5ix3 + x4)) = 0 Reorder the terms: 5(80ix + -80ix + -5ix3 + 5ix3 + 400i2 + -25i2x2 + -16x2 + x4) = 0 Combine like terms: 80ix + -80ix = 0 5(0 + -5ix3 + 5ix3 + 400i2 + -25i2x2 + -16x2 + x4) = 0 5(-5ix3 + 5ix3 + 400i2 + -25i2x2 + -16x2 + x4) = 0 Combine like terms: -5ix3 + 5ix3 = 0 5(0 + 400i2 + -25i2x2 + -16x2 + x4) = 0 5(400i2 + -25i2x2 + -16x2 + x4) = 0 (400i2 * 5 + -25i2x2 * 5 + -16x2 * 5 + x4 * 5) = 0 (2000i2 + -125i2x2 + -80x2 + 5x4) = 0 Solving 2000i2 + -125i2x2 + -80x2 + 5x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '80x2' to each side of the equation. 2000i2 + -125i2x2 + -80x2 + 80x2 + 5x4 = 0 + 80x2 Combine like terms: -80x2 + 80x2 = 0 2000i2 + -125i2x2 + 0 + 5x4 = 0 + 80x2 2000i2 + -125i2x2 + 5x4 = 0 + 80x2 Remove the zero: 2000i2 + -125i2x2 + 5x4 = 80x2 Add '-5x4' to each side of the equation. 2000i2 + -125i2x2 + 5x4 + -5x4 = 80x2 + -5x4 Combine like terms: 5x4 + -5x4 = 0 2000i2 + -125i2x2 + 0 = 80x2 + -5x4 2000i2 + -125i2x2 = 80x2 + -5x4 Reorder the terms: 2000i2 + -125i2x2 + -80x2 + 5x4 = 80x2 + -80x2 + -5x4 + 5x4 Combine like terms: 80x2 + -80x2 = 0 2000i2 + -125i2x2 + -80x2 + 5x4 = 0 + -5x4 + 5x4 2000i2 + -125i2x2 + -80x2 + 5x4 = -5x4 + 5x4 Combine like terms: -5x4 + 5x4 = 0 2000i2 + -125i2x2 + -80x2 + 5x4 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(400i2 + -25i2x2 + -16x2 + x4) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(400i2 + -25i2x2 + -16x2 + x4)' equal to zero and attempt to solve: Simplifying 400i2 + -25i2x2 + -16x2 + x4 = 0 Solving 400i2 + -25i2x2 + -16x2 + x4 = 0 Move all terms containing i to the left, all other terms to the right. Add '16x2' to each side of the equation. 400i2 + -25i2x2 + -16x2 + 16x2 + x4 = 0 + 16x2 Combine like terms: -16x2 + 16x2 = 0 400i2 + -25i2x2 + 0 + x4 = 0 + 16x2 400i2 + -25i2x2 + x4 = 0 + 16x2 Remove the zero: 400i2 + -25i2x2 + x4 = 16x2 Add '-1x4' to each side of the equation. 400i2 + -25i2x2 + x4 + -1x4 = 16x2 + -1x4 Combine like terms: x4 + -1x4 = 0 400i2 + -25i2x2 + 0 = 16x2 + -1x4 400i2 + -25i2x2 = 16x2 + -1x4 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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