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Simplifying -3i * 6i + -3(7 + 6i) = 0 Reorder the terms for easier multiplication: -3 * 6i * i + -3(7 + 6i) = 0 Multiply -3 * 6 -18i * i + -3(7 + 6i) = 0 Multiply i * i -18i2 + -3(7 + 6i) = 0 -18i2 + (7 * -3 + 6i * -3) = 0 -18i2 + (-21 + -18i) = 0 Reorder the terms: -21 + -18i + -18i2 = 0 Solving -21 + -18i + -18i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-3'. -3(7 + 6i + 6i2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(7 + 6i + 6i2)' equal to zero and attempt to solve: Simplifying 7 + 6i + 6i2 = 0 Solving 7 + 6i + 6i2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.166666667 + i + i2 = 0 Move the constant term to the right: Add '-1.166666667' to each side of the equation. 1.166666667 + i + -1.166666667 + i2 = 0 + -1.166666667 Reorder the terms: 1.166666667 + -1.166666667 + i + i2 = 0 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + i + i2 = 0 + -1.166666667 i + i2 = 0 + -1.166666667 Combine like terms: 0 + -1.166666667 = -1.166666667 i + i2 = -1.166666667 The i term is i. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + i2 = -1.166666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + i2 = -1.166666667 + 0.25 Combine like terms: -1.166666667 + 0.25 = -0.916666667 1.25 + i2 = -0.916666667 Factor a perfect square on the left side: (i + 0.5)(i + 0.5) = -0.916666667 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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