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Simplifying (x4 + -4)(x4 + 27ix) = 0 Reorder the terms: (-4 + x4)(x4 + 27ix) = 0 Reorder the terms: (-4 + x4)(27ix + x4) = 0 Multiply (-4 + x4) * (27ix + x4) (-4(27ix + x4) + x4(27ix + x4)) = 0 ((27ix * -4 + x4 * -4) + x4(27ix + x4)) = 0 ((-108ix + -4x4) + x4(27ix + x4)) = 0 (-108ix + -4x4 + (27ix * x4 + x4 * x4)) = 0 (-108ix + -4x4 + (27ix5 + x8)) = 0 Reorder the terms: (-108ix + 27ix5 + -4x4 + x8) = 0 (-108ix + 27ix5 + -4x4 + x8) = 0 Solving -108ix + 27ix5 + -4x4 + x8 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '4x4' to each side of the equation. -108ix + 27ix5 + -4x4 + 4x4 + x8 = 0 + 4x4 Combine like terms: -4x4 + 4x4 = 0 -108ix + 27ix5 + 0 + x8 = 0 + 4x4 -108ix + 27ix5 + x8 = 0 + 4x4 Remove the zero: -108ix + 27ix5 + x8 = 4x4 Add '-1x8' to each side of the equation. -108ix + 27ix5 + x8 + -1x8 = 4x4 + -1x8 Combine like terms: x8 + -1x8 = 0 -108ix + 27ix5 + 0 = 4x4 + -1x8 -108ix + 27ix5 = 4x4 + -1x8 Reorder the terms: -108ix + 27ix5 + -4x4 + x8 = 4x4 + -4x4 + -1x8 + x8 Combine like terms: 4x4 + -4x4 = 0 -108ix + 27ix5 + -4x4 + x8 = 0 + -1x8 + x8 -108ix + 27ix5 + -4x4 + x8 = -1x8 + x8 Combine like terms: -1x8 + x8 = 0 -108ix + 27ix5 + -4x4 + x8 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-108i + 27ix4 + -4x3 + x7) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing i to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-108i + 27ix4 + -4x3 + x7)' equal to zero and attempt to solve: Simplifying -108i + 27ix4 + -4x3 + x7 = 0 Solving -108i + 27ix4 + -4x3 + x7 = 0 Move all terms containing i to the left, all other terms to the right. Add '4x3' to each side of the equation. -108i + 27ix4 + -4x3 + 4x3 + x7 = 0 + 4x3 Combine like terms: -4x3 + 4x3 = 0 -108i + 27ix4 + 0 + x7 = 0 + 4x3 -108i + 27ix4 + x7 = 0 + 4x3 Remove the zero: -108i + 27ix4 + x7 = 4x3 Add '-1x7' to each side of the equation. -108i + 27ix4 + x7 + -1x7 = 4x3 + -1x7 Combine like terms: x7 + -1x7 = 0 -108i + 27ix4 + 0 = 4x3 + -1x7 -108i + 27ix4 = 4x3 + -1x7 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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