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Simplifying j2 + -2j + -41 = 0 Reorder the terms: -41 + -2j + j2 = 0 Solving -41 + -2j + 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 + -2j + 41 + j2 = 0 + 41 Reorder the terms: -41 + 41 + -2j + j2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -2j + j2 = 0 + 41 -2j + j2 = 0 + 41 Combine like terms: 0 + 41 = 41 -2j + j2 = 41 The j term is -2j. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2j + 1 + j2 = 41 + 1 Reorder the terms: 1 + -2j + j2 = 41 + 1 Combine like terms: 41 + 1 = 42 1 + -2j + j2 = 42 Factor a perfect square on the left side: (j + -1)(j + -1) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (j + -1) equal to 6.480740698 and -6.480740698.Subproblem 1
j + -1 = 6.480740698 Simplifying j + -1 = 6.480740698 Reorder the terms: -1 + j = 6.480740698 Solving -1 + j = 6.480740698 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + j = 6.480740698 + 1 Combine like terms: -1 + 1 = 0 0 + j = 6.480740698 + 1 j = 6.480740698 + 1 Combine like terms: 6.480740698 + 1 = 7.480740698 j = 7.480740698 Simplifying j = 7.480740698Subproblem 2
j + -1 = -6.480740698 Simplifying j + -1 = -6.480740698 Reorder the terms: -1 + j = -6.480740698 Solving -1 + j = -6.480740698 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + j = -6.480740698 + 1 Combine like terms: -1 + 1 = 0 0 + j = -6.480740698 + 1 j = -6.480740698 + 1 Combine like terms: -6.480740698 + 1 = -5.480740698 j = -5.480740698 Simplifying j = -5.480740698Solution
The solution to the problem is based on the solutions from the subproblems. j = {7.480740698, -5.480740698}
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