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Simplifying j2 + -14j = 27 Reorder the terms: -14j + j2 = 27 Solving -14j + j2 = 27 Solving for variable 'j'. Reorder the terms: -27 + -14j + j2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + -14j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -14j + 27 + j2 = 0 + 27 Reorder the terms: -27 + 27 + -14j + j2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -14j + j2 = 0 + 27 -14j + j2 = 0 + 27 Combine like terms: 0 + 27 = 27 -14j + j2 = 27 The j term is -14j. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14j + 49 + j2 = 27 + 49 Reorder the terms: 49 + -14j + j2 = 27 + 49 Combine like terms: 27 + 49 = 76 49 + -14j + j2 = 76 Factor a perfect square on the left side: (j + -7)(j + -7) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (j + -7) equal to 8.717797887 and -8.717797887.Subproblem 1
j + -7 = 8.717797887 Simplifying j + -7 = 8.717797887 Reorder the terms: -7 + j = 8.717797887 Solving -7 + j = 8.717797887 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + j = 8.717797887 + 7 Combine like terms: -7 + 7 = 0 0 + j = 8.717797887 + 7 j = 8.717797887 + 7 Combine like terms: 8.717797887 + 7 = 15.717797887 j = 15.717797887 Simplifying j = 15.717797887Subproblem 2
j + -7 = -8.717797887 Simplifying j + -7 = -8.717797887 Reorder the terms: -7 + j = -8.717797887 Solving -7 + j = -8.717797887 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + j = -8.717797887 + 7 Combine like terms: -7 + 7 = 0 0 + j = -8.717797887 + 7 j = -8.717797887 + 7 Combine like terms: -8.717797887 + 7 = -1.717797887 j = -1.717797887 Simplifying j = -1.717797887Solution
The solution to the problem is based on the solutions from the subproblems. j = {15.717797887, -1.717797887}
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