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Simplifying 3j2 + 18j + 1 = 0 Reorder the terms: 1 + 18j + 3j2 = 0 Solving 1 + 18j + 3j2 = 0 Solving for variable 'j'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + 6j + j2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 6j + -0.3333333333 + j2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 6j + j2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 6j + j2 = 0 + -0.3333333333 6j + j2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 6j + j2 = -0.3333333333 The j term is 6j. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6j + 9 + j2 = -0.3333333333 + 9 Reorder the terms: 9 + 6j + j2 = -0.3333333333 + 9 Combine like terms: -0.3333333333 + 9 = 8.6666666667 9 + 6j + j2 = 8.6666666667 Factor a perfect square on the left side: (j + 3)(j + 3) = 8.6666666667 Calculate the square root of the right side: 2.943920289 Break this problem into two subproblems by setting (j + 3) equal to 2.943920289 and -2.943920289.Subproblem 1
j + 3 = 2.943920289 Simplifying j + 3 = 2.943920289 Reorder the terms: 3 + j = 2.943920289 Solving 3 + j = 2.943920289 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + j = 2.943920289 + -3 Combine like terms: 3 + -3 = 0 0 + j = 2.943920289 + -3 j = 2.943920289 + -3 Combine like terms: 2.943920289 + -3 = -0.056079711 j = -0.056079711 Simplifying j = -0.056079711Subproblem 2
j + 3 = -2.943920289 Simplifying j + 3 = -2.943920289 Reorder the terms: 3 + j = -2.943920289 Solving 3 + j = -2.943920289 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + j = -2.943920289 + -3 Combine like terms: 3 + -3 = 0 0 + j = -2.943920289 + -3 j = -2.943920289 + -3 Combine like terms: -2.943920289 + -3 = -5.943920289 j = -5.943920289 Simplifying j = -5.943920289Solution
The solution to the problem is based on the solutions from the subproblems. j = {-0.056079711, -5.943920289}
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