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Simplifying 9j2 + -9j + -6 = 0 Reorder the terms: -6 + -9j + 9j2 = 0 Solving -6 + -9j + 9j2 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + -3j + 3j2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -3j + 3j2)' equal to zero and attempt to solve: Simplifying -2 + -3j + 3j2 = 0 Solving -2 + -3j + 3j2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + -1j + j2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -1j + 0.6666666667 + j2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -1j + j2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -1j + j2 = 0 + 0.6666666667 -1j + j2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -1j + j2 = 0.6666666667 The j term is -1j. 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. -1j + 0.25 + j2 = 0.6666666667 + 0.25 Reorder the terms: 0.25 + -1j + j2 = 0.6666666667 + 0.25 Combine like terms: 0.6666666667 + 0.25 = 0.9166666667 0.25 + -1j + j2 = 0.9166666667 Factor a perfect square on the left side: (j + -0.5)(j + -0.5) = 0.9166666667 Calculate the square root of the right side: 0.957427108 Break this problem into two subproblems by setting (j + -0.5) equal to 0.957427108 and -0.957427108.Subproblem 1
j + -0.5 = 0.957427108 Simplifying j + -0.5 = 0.957427108 Reorder the terms: -0.5 + j = 0.957427108 Solving -0.5 + j = 0.957427108 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + j = 0.957427108 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + j = 0.957427108 + 0.5 j = 0.957427108 + 0.5 Combine like terms: 0.957427108 + 0.5 = 1.457427108 j = 1.457427108 Simplifying j = 1.457427108Subproblem 2
j + -0.5 = -0.957427108 Simplifying j + -0.5 = -0.957427108 Reorder the terms: -0.5 + j = -0.957427108 Solving -0.5 + j = -0.957427108 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + j = -0.957427108 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + j = -0.957427108 + 0.5 j = -0.957427108 + 0.5 Combine like terms: -0.957427108 + 0.5 = -0.457427108 j = -0.457427108 Simplifying j = -0.457427108Solution
The solution to the problem is based on the solutions from the subproblems. j = {1.457427108, -0.457427108}Solution
j = {1.457427108, -0.457427108}
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