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Simplifying -9i(-9i + 4) + 3(8 + 8i) = -57i + -12i Reorder the terms: -9i(4 + -9i) + 3(8 + 8i) = -57i + -12i (4 * -9i + -9i * -9i) + 3(8 + 8i) = -57i + -12i (-36i + 81i2) + 3(8 + 8i) = -57i + -12i -36i + 81i2 + (8 * 3 + 8i * 3) = -57i + -12i -36i + 81i2 + (24 + 24i) = -57i + -12i Reorder the terms: 24 + -36i + 24i + 81i2 = -57i + -12i Combine like terms: -36i + 24i = -12i 24 + -12i + 81i2 = -57i + -12i Combine like terms: -57i + -12i = -69i 24 + -12i + 81i2 = -69i Solving 24 + -12i + 81i2 = -69i Solving for variable 'i'. Reorder the terms: 24 + -12i + 69i + 81i2 = -69i + 69i Combine like terms: -12i + 69i = 57i 24 + 57i + 81i2 = -69i + 69i Combine like terms: -69i + 69i = 0 24 + 57i + 81i2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(8 + 19i + 27i2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(8 + 19i + 27i2)' equal to zero and attempt to solve: Simplifying 8 + 19i + 27i2 = 0 Solving 8 + 19i + 27i2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. 0.2962962963 + 0.7037037037i + i2 = 0 Move the constant term to the right: Add '-0.2962962963' to each side of the equation. 0.2962962963 + 0.7037037037i + -0.2962962963 + i2 = 0 + -0.2962962963 Reorder the terms: 0.2962962963 + -0.2962962963 + 0.7037037037i + i2 = 0 + -0.2962962963 Combine like terms: 0.2962962963 + -0.2962962963 = 0.0000000000 0.0000000000 + 0.7037037037i + i2 = 0 + -0.2962962963 0.7037037037i + i2 = 0 + -0.2962962963 Combine like terms: 0 + -0.2962962963 = -0.2962962963 0.7037037037i + i2 = -0.2962962963 The i term is 0.7037037037i. Take half its coefficient (0.3518518519). Square it (0.1237997257) and add it to both sides. Add '0.1237997257' to each side of the equation. 0.7037037037i + 0.1237997257 + i2 = -0.2962962963 + 0.1237997257 Reorder the terms: 0.1237997257 + 0.7037037037i + i2 = -0.2962962963 + 0.1237997257 Combine like terms: -0.2962962963 + 0.1237997257 = -0.1724965706 0.1237997257 + 0.7037037037i + i2 = -0.1724965706 Factor a perfect square on the left side: (i + 0.3518518519)(i + 0.3518518519) = -0.1724965706 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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