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Simplifying -9i(-9i + 4) + 3(8 + 8i) = 0 Reorder the terms: -9i(4 + -9i) + 3(8 + 8i) = 0 (4 * -9i + -9i * -9i) + 3(8 + 8i) = 0 (-36i + 81i2) + 3(8 + 8i) = 0 -36i + 81i2 + (8 * 3 + 8i * 3) = 0 -36i + 81i2 + (24 + 24i) = 0 Reorder the terms: 24 + -36i + 24i + 81i2 = 0 Combine like terms: -36i + 24i = -12i 24 + -12i + 81i2 = 0 Solving 24 + -12i + 81i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(8 + -4i + 27i2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(8 + -4i + 27i2)' equal to zero and attempt to solve: Simplifying 8 + -4i + 27i2 = 0 Solving 8 + -4i + 27i2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. 0.2962962963 + -0.1481481481i + i2 = 0 Move the constant term to the right: Add '-0.2962962963' to each side of the equation. 0.2962962963 + -0.1481481481i + -0.2962962963 + i2 = 0 + -0.2962962963 Reorder the terms: 0.2962962963 + -0.2962962963 + -0.1481481481i + i2 = 0 + -0.2962962963 Combine like terms: 0.2962962963 + -0.2962962963 = 0.0000000000 0.0000000000 + -0.1481481481i + i2 = 0 + -0.2962962963 -0.1481481481i + i2 = 0 + -0.2962962963 Combine like terms: 0 + -0.2962962963 = -0.2962962963 -0.1481481481i + i2 = -0.2962962963 The i term is -0.1481481481i. Take half its coefficient (-0.07407407405). Square it (0.005486968446) and add it to both sides. Add '0.005486968446' to each side of the equation. -0.1481481481i + 0.005486968446 + i2 = -0.2962962963 + 0.005486968446 Reorder the terms: 0.005486968446 + -0.1481481481i + i2 = -0.2962962963 + 0.005486968446 Combine like terms: -0.2962962963 + 0.005486968446 = -0.290809327854 0.005486968446 + -0.1481481481i + i2 = -0.290809327854 Factor a perfect square on the left side: (i + -0.07407407405)(i + -0.07407407405) = -0.290809327854 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. The solution to this equation could not be determined.
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