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Simplifying 11j + -1j2 = 17 Solving 11j + -1j2 = 17 Solving for variable 'j'. Reorder the terms: -17 + 11j + -1j2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + 11j + -1j2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 17 + -11j + j2 = 0 Move the constant term to the right: Add '-17' to each side of the equation. 17 + -11j + -17 + j2 = 0 + -17 Reorder the terms: 17 + -17 + -11j + j2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -11j + j2 = 0 + -17 -11j + j2 = 0 + -17 Combine like terms: 0 + -17 = -17 -11j + j2 = -17 The j term is -11j. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11j + 30.25 + j2 = -17 + 30.25 Reorder the terms: 30.25 + -11j + j2 = -17 + 30.25 Combine like terms: -17 + 30.25 = 13.25 30.25 + -11j + j2 = 13.25 Factor a perfect square on the left side: (j + -5.5)(j + -5.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (j + -5.5) equal to 3.640054945 and -3.640054945.Subproblem 1
j + -5.5 = 3.640054945 Simplifying j + -5.5 = 3.640054945 Reorder the terms: -5.5 + j = 3.640054945 Solving -5.5 + j = 3.640054945 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + j = 3.640054945 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + j = 3.640054945 + 5.5 j = 3.640054945 + 5.5 Combine like terms: 3.640054945 + 5.5 = 9.140054945 j = 9.140054945 Simplifying j = 9.140054945Subproblem 2
j + -5.5 = -3.640054945 Simplifying j + -5.5 = -3.640054945 Reorder the terms: -5.5 + j = -3.640054945 Solving -5.5 + j = -3.640054945 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + j = -3.640054945 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + j = -3.640054945 + 5.5 j = -3.640054945 + 5.5 Combine like terms: -3.640054945 + 5.5 = 1.859945055 j = 1.859945055 Simplifying j = 1.859945055Solution
The solution to the problem is based on the solutions from the subproblems. j = {9.140054945, 1.859945055}
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