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Simplifying 3i(5i2 + 8i + 9) = 0 Reorder the terms: 3i(9 + 8i + 5i2) = 0 (9 * 3i + 8i * 3i + 5i2 * 3i) = 0 (27i + 24i2 + 15i3) = 0 Solving 27i + 24i2 + 15i3 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3i'. 3i(9 + 8i + 5i2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'i' equal to zero and attempt to solve: Simplifying i = 0 Solving i = 0 Move all terms containing i to the left, all other terms to the right. Simplifying i = 0Subproblem 2
Set the factor '(9 + 8i + 5i2)' equal to zero and attempt to solve: Simplifying 9 + 8i + 5i2 = 0 Solving 9 + 8i + 5i2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.8 + 1.6i + i2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + 1.6i + -1.8 + i2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + 1.6i + i2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + 1.6i + i2 = 0 + -1.8 1.6i + i2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 1.6i + i2 = -1.8 The i term is 1.6i. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6i + 0.64 + i2 = -1.8 + 0.64 Reorder the terms: 0.64 + 1.6i + i2 = -1.8 + 0.64 Combine like terms: -1.8 + 0.64 = -1.16 0.64 + 1.6i + i2 = -1.16 Factor a perfect square on the left side: (i + 0.8)(i + 0.8) = -1.16 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
i = {0}
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