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Simplifying j2 + -19j + 38 = 0 Reorder the terms: 38 + -19j + j2 = 0 Solving 38 + -19j + j2 = 0 Solving for variable 'j'. Begin completing the square. Move the constant term to the right: Add '-38' to each side of the equation. 38 + -19j + -38 + j2 = 0 + -38 Reorder the terms: 38 + -38 + -19j + j2 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + -19j + j2 = 0 + -38 -19j + j2 = 0 + -38 Combine like terms: 0 + -38 = -38 -19j + j2 = -38 The j term is -19j. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19j + 90.25 + j2 = -38 + 90.25 Reorder the terms: 90.25 + -19j + j2 = -38 + 90.25 Combine like terms: -38 + 90.25 = 52.25 90.25 + -19j + j2 = 52.25 Factor a perfect square on the left side: (j + -9.5)(j + -9.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (j + -9.5) equal to 7.228416147 and -7.228416147.Subproblem 1
j + -9.5 = 7.228416147 Simplifying j + -9.5 = 7.228416147 Reorder the terms: -9.5 + j = 7.228416147 Solving -9.5 + j = 7.228416147 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + j = 7.228416147 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + j = 7.228416147 + 9.5 j = 7.228416147 + 9.5 Combine like terms: 7.228416147 + 9.5 = 16.728416147 j = 16.728416147 Simplifying j = 16.728416147Subproblem 2
j + -9.5 = -7.228416147 Simplifying j + -9.5 = -7.228416147 Reorder the terms: -9.5 + j = -7.228416147 Solving -9.5 + j = -7.228416147 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + j = -7.228416147 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + j = -7.228416147 + 9.5 j = -7.228416147 + 9.5 Combine like terms: -7.228416147 + 9.5 = 2.271583853 j = 2.271583853 Simplifying j = 2.271583853Solution
The solution to the problem is based on the solutions from the subproblems. j = {16.728416147, 2.271583853}
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