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Simplifying j2 + -6j + -3 = 0 Reorder the terms: -3 + -6j + j2 = 0 Solving -3 + -6j + j2 = 0 Solving for variable 'j'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -6j + 3 + j2 = 0 + 3 Reorder the terms: -3 + 3 + -6j + j2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -6j + j2 = 0 + 3 -6j + j2 = 0 + 3 Combine like terms: 0 + 3 = 3 -6j + j2 = 3 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 = 3 + 9 Reorder the terms: 9 + -6j + j2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + -6j + j2 = 12 Factor a perfect square on the left side: (j + -3)(j + -3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (j + -3) equal to 3.464101615 and -3.464101615.Subproblem 1
j + -3 = 3.464101615 Simplifying j + -3 = 3.464101615 Reorder the terms: -3 + j = 3.464101615 Solving -3 + j = 3.464101615 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 = 3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + j = 3.464101615 + 3 j = 3.464101615 + 3 Combine like terms: 3.464101615 + 3 = 6.464101615 j = 6.464101615 Simplifying j = 6.464101615Subproblem 2
j + -3 = -3.464101615 Simplifying j + -3 = -3.464101615 Reorder the terms: -3 + j = -3.464101615 Solving -3 + j = -3.464101615 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 = -3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + j = -3.464101615 + 3 j = -3.464101615 + 3 Combine like terms: -3.464101615 + 3 = -0.464101615 j = -0.464101615 Simplifying j = -0.464101615Solution
The solution to the problem is based on the solutions from the subproblems. j = {6.464101615, -0.464101615}
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