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Simplifying a[x + -1(-1)][x + -1(-3 + -5i)][x + -1(-3 + 5i)] = 0 Multiply -1 * -1 a[x + 1][x + -1(-3 + -5i)][x + -1(-3 + 5i)] = 0 Reorder the terms: a[1 + x][x + -1(-3 + -5i)][x + -1(-3 + 5i)] = 0 a[1 + x][x + (-3 * -1 + -5i * -1)][x + -1(-3 + 5i)] = 0 a[1 + x][x + (3 + 5i)][x + -1(-3 + 5i)] = 0 Reorder the terms: a[1 + x][3 + 5i + x][x + -1(-3 + 5i)] = 0 a[1 + x][3 + 5i + x][x + (-3 * -1 + 5i * -1)] = 0 a[1 + x][3 + 5i + x][x + (3 + -5i)] = 0 Reorder the terms: a[1 + x][3 + 5i + x][3 + -5i + x] = 0 Multiply [1 + x] * [3 + 5i + x] a[1[3 + 5i + x] + x[3 + 5i + x]][3 + -5i + x] = 0 a[[3 * 1 + 5i * 1 + x * 1] + x[3 + 5i + x]][3 + -5i + x] = 0 a[[3 + 5i + 1x] + x[3 + 5i + x]][3 + -5i + x] = 0 a[3 + 5i + 1x + [3 * x + 5i * x + x * x]][3 + -5i + x] = 0 Reorder the terms: a[3 + 5i + 1x + [5ix + 3x + x2]][3 + -5i + x] = 0 a[3 + 5i + 1x + [5ix + 3x + x2]][3 + -5i + x] = 0 Reorder the terms: a[3 + 5i + 5ix + 1x + 3x + x2][3 + -5i + x] = 0 Combine like terms: 1x + 3x = 4x a[3 + 5i + 5ix + 4x + x2][3 + -5i + x] = 0 Multiply [3 + 5i + 5ix + 4x + x2] * [3 + -5i + x] a[3[3 + -5i + x] + 5i * [3 + -5i + x] + 5ix * [3 + -5i + x] + 4x * [3 + -5i + x] + x2[3 + -5i + x]] = 0 a[[3 * 3 + -5i * 3 + x * 3] + 5i * [3 + -5i + x] + 5ix * [3 + -5i + x] + 4x * [3 + -5i + x] + x2[3 + -5i + x]] = 0 a[[9 + -15i + 3x] + 5i * [3 + -5i + x] + 5ix * [3 + -5i + x] + 4x * [3 + -5i + x] + x2[3 + -5i + x]] = 0 a[9 + -15i + 3x + [3 * 5i + -5i * 5i + x * 5i] + 5ix * [3 + -5i + x] + 4x * [3 + -5i + x] + x2[3 + -5i + x]] = 0 Reorder the terms: a[9 + -15i + 3x + [15i + 5ix + -25i2] + 5ix * [3 + -5i + x] + 4x * [3 + -5i + x] + x2[3 + -5i + x]] = 0 a[9 + -15i + 3x + [15i + 5ix + -25i2] + 5ix * [3 + -5i + x] + 4x * [3 + -5i + x] + x2[3 + -5i + x]] = 0 a[9 + -15i + 3x + 15i + 5ix + -25i2 + [3 * 5ix + -5i * 5ix + x * 5ix] + 4x * [3 + -5i + x] + x2[3 + -5i + x]] = 0 Reorder the terms: a[9 + -15i + 3x + 15i + 5ix + -25i2 + [15ix + 5ix2 + -25i2x] + 4x * [3 + -5i + x] + x2[3 + -5i + x]] = 0 a[9 + -15i + 3x + 15i + 5ix + -25i2 + [15ix + 5ix2 + -25i2x] + 4x * [3 + -5i + x] + x2[3 + -5i + x]] = 0 a[9 + -15i + 3x + 15i + 5ix + -25i2 + 15ix + 5ix2 + -25i2x + [3 * 4x + -5i * 4x + x * 4x] + x2[3 + -5i + x]] = 0 Reorder the terms: a[9 + -15i + 3x + 15i + 5ix + -25i2 + 15ix + 5ix2 + -25i2x + [-20ix + 12x + 4x2] + x2[3 + -5i + x]] = 0 a[9 + -15i + 3x + 15i + 5ix + -25i2 + 15ix + 5ix2 + -25i2x + [-20ix + 12x + 4x2] + x2[3 + -5i + x]] = 0 a[9 + -15i + 3x + 15i + 5ix + -25i2 + 15ix + 5ix2 + -25i2x + -20ix + 12x + 4x2 + [3 * x2 + -5i * x2 + x * x2]] = 0 Reorder the terms: a[9 + -15i + 3x + 15i + 5ix + -25i2 + 15ix + 5ix2 + -25i2x + -20ix + 12x + 4x2 + [-5ix2 + 3x2 + x3]] = 0 a[9 + -15i + 3x + 15i + 5ix + -25i2 + 15ix + 5ix2 + -25i2x + -20ix + 12x + 4x2 + [-5ix2 + 3x2 + x3]] = 0 Reorder the terms: a[9 + -15i + 15i + 5ix + 15ix + -20ix + 5ix2 + -5ix2 + -25i2 + -25i2x + 3x + 12x + 4x2 + 3x2 + x3] = 0 Combine like terms: -15i + 15i = 0 a[9 + 0 + 5ix + 15ix + -20ix + 5ix2 + -5ix2 + -25i2 + -25i2x + 3x + 12x + 4x2 + 3x2 + x3] = 0 a[9 + 5ix + 15ix + -20ix + 5ix2 + -5ix2 + -25i2 + -25i2x + 3x + 12x + 4x2 + 3x2 + x3] = 0 Combine like terms: 5ix + 15ix = 20ix a[9 + 20ix + -20ix + 5ix2 + -5ix2 + -25i2 + -25i2x + 3x + 12x + 4x2 + 3x2 + x3] = 0 Combine like terms: 20ix + -20ix = 0 a[9 + 0 + 5ix2 + -5ix2 + -25i2 + -25i2x + 3x + 12x + 4x2 + 3x2 + x3] = 0 a[9 + 5ix2 + -5ix2 + -25i2 + -25i2x + 3x + 12x + 4x2 + 3x2 + x3] = 0 Combine like terms: 5ix2 + -5ix2 = 0 a[9 + 0 + -25i2 + -25i2x + 3x + 12x + 4x2 + 3x2 + x3] = 0 a[9 + -25i2 + -25i2x + 3x + 12x + 4x2 + 3x2 + x3] = 0 Combine like terms: 3x + 12x = 15x a[9 + -25i2 + -25i2x + 15x + 4x2 + 3x2 + x3] = 0 Combine like terms: 4x2 + 3x2 = 7x2 a[9 + -25i2 + -25i2x + 15x + 7x2 + x3] = 0 [9 * a + -25i2 * a + -25i2x * a + 15x * a + 7x2 * a + x3 * a] = 0 [9a + -25ai2 + -25ai2x + 15ax + 7ax2 + ax3] = 0 Solving 9a + -25ai2 + -25ai2x + 15ax + 7ax2 + ax3 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'a'. a(9 + -25i2 + -25i2x + 15x + 7x2 + x3) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(9 + -25i2 + -25i2x + 15x + 7x2 + x3)' equal to zero and attempt to solve: Simplifying 9 + -25i2 + -25i2x + 15x + 7x2 + x3 = 0 Solving 9 + -25i2 + -25i2x + 15x + 7x2 + x3 = 0 Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -25i2 + -25i2x + 15x + 7x2 + -9 + x3 = 0 + -9 Reorder the terms: 9 + -9 + -25i2 + -25i2x + 15x + 7x2 + x3 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -25i2 + -25i2x + 15x + 7x2 + x3 = 0 + -9 -25i2 + -25i2x + 15x + 7x2 + x3 = 0 + -9 Combine like terms: 0 + -9 = -9 -25i2 + -25i2x + 15x + 7x2 + x3 = -9 Add '25i2' to each side of the equation. -25i2 + -25i2x + 15x + 7x2 + 25i2 + x3 = -9 + 25i2 Reorder the terms: -25i2 + 25i2 + -25i2x + 15x + 7x2 + x3 = -9 + 25i2 Combine like terms: -25i2 + 25i2 = 0 0 + -25i2x + 15x + 7x2 + x3 = -9 + 25i2 -25i2x + 15x + 7x2 + x3 = -9 + 25i2 Add '25i2x' to each side of the equation. -25i2x + 15x + 7x2 + 25i2x + x3 = -9 + 25i2 + 25i2x Reorder the terms: -25i2x + 25i2x + 15x + 7x2 + x3 = -9 + 25i2 + 25i2x Combine like terms: -25i2x + 25i2x = 0 0 + 15x + 7x2 + x3 = -9 + 25i2 + 25i2x 15x + 7x2 + x3 = -9 + 25i2 + 25i2x Add '-15x' to each side of the equation. 15x + 7x2 + -15x + x3 = -9 + 25i2 + 25i2x + -15x Reorder the terms: 15x + -15x + 7x2 + x3 = -9 + 25i2 + 25i2x + -15x Combine like terms: 15x + -15x = 0 0 + 7x2 + x3 = -9 + 25i2 + 25i2x + -15x 7x2 + x3 = -9 + 25i2 + 25i2x + -15x Add '-7x2' to each side of the equation. 7x2 + -7x2 + x3 = -9 + 25i2 + 25i2x + -15x + -7x2 Combine like terms: 7x2 + -7x2 = 0 0 + x3 = -9 + 25i2 + 25i2x + -15x + -7x2 x3 = -9 + 25i2 + 25i2x + -15x + -7x2 Add '-1x3' to each side of the equation. x3 + -1x3 = -9 + 25i2 + 25i2x + -15x + -7x2 + -1x3 Combine like terms: x3 + -1x3 = 0 0 = -9 + 25i2 + 25i2x + -15x + -7x2 + -1x3 Simplifying 0 = -9 + 25i2 + 25i2x + -15x + -7x2 + -1x3 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
a = {0}
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