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Simplifying j2 + 7j + 9 = 57 Reorder the terms: 9 + 7j + j2 = 57 Solving 9 + 7j + j2 = 57 Solving for variable 'j'. Reorder the terms: 9 + -57 + 7j + j2 = 57 + -57 Combine like terms: 9 + -57 = -48 -48 + 7j + j2 = 57 + -57 Combine like terms: 57 + -57 = 0 -48 + 7j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 7j + 48 + j2 = 0 + 48 Reorder the terms: -48 + 48 + 7j + j2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 7j + j2 = 0 + 48 7j + j2 = 0 + 48 Combine like terms: 0 + 48 = 48 7j + j2 = 48 The j term is 7j. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7j + 12.25 + j2 = 48 + 12.25 Reorder the terms: 12.25 + 7j + j2 = 48 + 12.25 Combine like terms: 48 + 12.25 = 60.25 12.25 + 7j + j2 = 60.25 Factor a perfect square on the left side: (j + 3.5)(j + 3.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (j + 3.5) equal to 7.762087348 and -7.762087348.Subproblem 1
j + 3.5 = 7.762087348 Simplifying j + 3.5 = 7.762087348 Reorder the terms: 3.5 + j = 7.762087348 Solving 3.5 + j = 7.762087348 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + j = 7.762087348 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + j = 7.762087348 + -3.5 j = 7.762087348 + -3.5 Combine like terms: 7.762087348 + -3.5 = 4.262087348 j = 4.262087348 Simplifying j = 4.262087348Subproblem 2
j + 3.5 = -7.762087348 Simplifying j + 3.5 = -7.762087348 Reorder the terms: 3.5 + j = -7.762087348 Solving 3.5 + j = -7.762087348 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + j = -7.762087348 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + j = -7.762087348 + -3.5 j = -7.762087348 + -3.5 Combine like terms: -7.762087348 + -3.5 = -11.262087348 j = -11.262087348 Simplifying j = -11.262087348Solution
The solution to the problem is based on the solutions from the subproblems. j = {4.262087348, -11.262087348}
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