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Simplifying 5(x + 3)(x + -3)(x + -5i)(x + 5i) = 0 Reorder the terms: 5(3 + x)(x + -3)(x + -5i)(x + 5i) = 0 Reorder the terms: 5(3 + x)(-3 + x)(x + -5i)(x + 5i) = 0 Reorder the terms: 5(3 + x)(-3 + x)(-5i + x)(x + 5i) = 0 Reorder the terms: 5(3 + x)(-3 + x)(-5i + x)(5i + x) = 0 Multiply (3 + x) * (-3 + x) 5(3(-3 + x) + x(-3 + x))(-5i + x)(5i + x) = 0 5((-3 * 3 + x * 3) + x(-3 + x))(-5i + x)(5i + x) = 0 5((-9 + 3x) + x(-3 + x))(-5i + x)(5i + x) = 0 5(-9 + 3x + (-3 * x + x * x))(-5i + x)(5i + x) = 0 5(-9 + 3x + (-3x + x2))(-5i + x)(5i + x) = 0 Combine like terms: 3x + -3x = 0 5(-9 + 0 + x2)(-5i + x)(5i + x) = 0 5(-9 + x2)(-5i + x)(5i + x) = 0 Multiply (-9 + x2) * (-5i + x) 5(-9(-5i + x) + x2(-5i + x))(5i + x) = 0 5((-5i * -9 + x * -9) + x2(-5i + x))(5i + x) = 0 5((45i + -9x) + x2(-5i + x))(5i + x) = 0 5(45i + -9x + (-5i * x2 + x * x2))(5i + x) = 0 5(45i + -9x + (-5ix2 + x3))(5i + x) = 0 Reorder the terms: 5(45i + -5ix2 + -9x + x3)(5i + x) = 0 5(45i + -5ix2 + -9x + x3)(5i + x) = 0 Multiply (45i + -5ix2 + -9x + x3) * (5i + x) 5(45i * (5i + x) + -5ix2 * (5i + x) + -9x * (5i + x) + x3(5i + x)) = 0 5((5i * 45i + x * 45i) + -5ix2 * (5i + x) + -9x * (5i + x) + x3(5i + x)) = 0 Reorder the terms: 5((45ix + 225i2) + -5ix2 * (5i + x) + -9x * (5i + x) + x3(5i + x)) = 0 5((45ix + 225i2) + -5ix2 * (5i + x) + -9x * (5i + x) + x3(5i + x)) = 0 5(45ix + 225i2 + (5i * -5ix2 + x * -5ix2) + -9x * (5i + x) + x3(5i + x)) = 0 Reorder the terms: 5(45ix + 225i2 + (-5ix3 + -25i2x2) + -9x * (5i + x) + x3(5i + x)) = 0 5(45ix + 225i2 + (-5ix3 + -25i2x2) + -9x * (5i + x) + x3(5i + x)) = 0 5(45ix + 225i2 + -5ix3 + -25i2x2 + (5i * -9x + x * -9x) + x3(5i + x)) = 0 5(45ix + 225i2 + -5ix3 + -25i2x2 + (-45ix + -9x2) + x3(5i + x)) = 0 5(45ix + 225i2 + -5ix3 + -25i2x2 + -45ix + -9x2 + (5i * x3 + x * x3)) = 0 5(45ix + 225i2 + -5ix3 + -25i2x2 + -45ix + -9x2 + (5ix3 + x4)) = 0 Reorder the terms: 5(45ix + -45ix + -5ix3 + 5ix3 + 225i2 + -25i2x2 + -9x2 + x4) = 0 Combine like terms: 45ix + -45ix = 0 5(0 + -5ix3 + 5ix3 + 225i2 + -25i2x2 + -9x2 + x4) = 0 5(-5ix3 + 5ix3 + 225i2 + -25i2x2 + -9x2 + x4) = 0 Combine like terms: -5ix3 + 5ix3 = 0 5(0 + 225i2 + -25i2x2 + -9x2 + x4) = 0 5(225i2 + -25i2x2 + -9x2 + x4) = 0 (225i2 * 5 + -25i2x2 * 5 + -9x2 * 5 + x4 * 5) = 0 (1125i2 + -125i2x2 + -45x2 + 5x4) = 0 Solving 1125i2 + -125i2x2 + -45x2 + 5x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '45x2' to each side of the equation. 1125i2 + -125i2x2 + -45x2 + 45x2 + 5x4 = 0 + 45x2 Combine like terms: -45x2 + 45x2 = 0 1125i2 + -125i2x2 + 0 + 5x4 = 0 + 45x2 1125i2 + -125i2x2 + 5x4 = 0 + 45x2 Remove the zero: 1125i2 + -125i2x2 + 5x4 = 45x2 Add '-5x4' to each side of the equation. 1125i2 + -125i2x2 + 5x4 + -5x4 = 45x2 + -5x4 Combine like terms: 5x4 + -5x4 = 0 1125i2 + -125i2x2 + 0 = 45x2 + -5x4 1125i2 + -125i2x2 = 45x2 + -5x4 Reorder the terms: 1125i2 + -125i2x2 + -45x2 + 5x4 = 45x2 + -45x2 + -5x4 + 5x4 Combine like terms: 45x2 + -45x2 = 0 1125i2 + -125i2x2 + -45x2 + 5x4 = 0 + -5x4 + 5x4 1125i2 + -125i2x2 + -45x2 + 5x4 = -5x4 + 5x4 Combine like terms: -5x4 + 5x4 = 0 1125i2 + -125i2x2 + -45x2 + 5x4 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(225i2 + -25i2x2 + -9x2 + x4) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(225i2 + -25i2x2 + -9x2 + x4)' equal to zero and attempt to solve: Simplifying 225i2 + -25i2x2 + -9x2 + x4 = 0 Solving 225i2 + -25i2x2 + -9x2 + x4 = 0 Move all terms containing i to the left, all other terms to the right. Add '9x2' to each side of the equation. 225i2 + -25i2x2 + -9x2 + 9x2 + x4 = 0 + 9x2 Combine like terms: -9x2 + 9x2 = 0 225i2 + -25i2x2 + 0 + x4 = 0 + 9x2 225i2 + -25i2x2 + x4 = 0 + 9x2 Remove the zero: 225i2 + -25i2x2 + x4 = 9x2 Add '-1x4' to each side of the equation. 225i2 + -25i2x2 + x4 + -1x4 = 9x2 + -1x4 Combine like terms: x4 + -1x4 = 0 225i2 + -25i2x2 + 0 = 9x2 + -1x4 225i2 + -25i2x2 = 9x2 + -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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