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Simplifying 9j2 + 6j + 1 = 0 Reorder the terms: 1 + 6j + 9j2 = 0 Solving 1 + 6j + 9j2 = 0 Solving for variable 'j'. Factor a trinomial. (1 + 3j)(1 + 3j) = 0Subproblem 1
Set the factor '(1 + 3j)' equal to zero and attempt to solve: Simplifying 1 + 3j = 0 Solving 1 + 3j = 0 Move all terms containing j to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3j = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3j = 0 + -1 3j = 0 + -1 Combine like terms: 0 + -1 = -1 3j = -1 Divide each side by '3'. j = -0.3333333333 Simplifying j = -0.3333333333Subproblem 2
Set the factor '(1 + 3j)' equal to zero and attempt to solve: Simplifying 1 + 3j = 0 Solving 1 + 3j = 0 Move all terms containing j to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3j = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3j = 0 + -1 3j = 0 + -1 Combine like terms: 0 + -1 = -1 3j = -1 Divide each side by '3'. j = -0.3333333333 Simplifying j = -0.3333333333Solution
j = {-0.3333333333, -0.3333333333}
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