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Simplifying j2 + -10j + -41 = 0 Reorder the terms: -41 + -10j + j2 = 0 Solving -41 + -10j + j2 = 0 Solving for variable 'j'. Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -10j + 41 + j2 = 0 + 41 Reorder the terms: -41 + 41 + -10j + j2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -10j + j2 = 0 + 41 -10j + j2 = 0 + 41 Combine like terms: 0 + 41 = 41 -10j + j2 = 41 The j term is -10j. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10j + 25 + j2 = 41 + 25 Reorder the terms: 25 + -10j + j2 = 41 + 25 Combine like terms: 41 + 25 = 66 25 + -10j + j2 = 66 Factor a perfect square on the left side: (j + -5)(j + -5) = 66 Calculate the square root of the right side: 8.124038405 Break this problem into two subproblems by setting (j + -5) equal to 8.124038405 and -8.124038405.Subproblem 1
j + -5 = 8.124038405 Simplifying j + -5 = 8.124038405 Reorder the terms: -5 + j = 8.124038405 Solving -5 + j = 8.124038405 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + j = 8.124038405 + 5 Combine like terms: -5 + 5 = 0 0 + j = 8.124038405 + 5 j = 8.124038405 + 5 Combine like terms: 8.124038405 + 5 = 13.124038405 j = 13.124038405 Simplifying j = 13.124038405Subproblem 2
j + -5 = -8.124038405 Simplifying j + -5 = -8.124038405 Reorder the terms: -5 + j = -8.124038405 Solving -5 + j = -8.124038405 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + j = -8.124038405 + 5 Combine like terms: -5 + 5 = 0 0 + j = -8.124038405 + 5 j = -8.124038405 + 5 Combine like terms: -8.124038405 + 5 = -3.124038405 j = -3.124038405 Simplifying j = -3.124038405Solution
The solution to the problem is based on the solutions from the subproblems. j = {13.124038405, -3.124038405}
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