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Simplifying j2 + -18j = -1 Reorder the terms: -18j + j2 = -1 Solving -18j + j2 = -1 Solving for variable 'j'. Reorder the terms: 1 + -18j + j2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + -18j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -18j + -1 + j2 = 0 + -1 Reorder the terms: 1 + -1 + -18j + j2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -18j + j2 = 0 + -1 -18j + j2 = 0 + -1 Combine like terms: 0 + -1 = -1 -18j + j2 = -1 The j term is -18j. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18j + 81 + j2 = -1 + 81 Reorder the terms: 81 + -18j + j2 = -1 + 81 Combine like terms: -1 + 81 = 80 81 + -18j + j2 = 80 Factor a perfect square on the left side: (j + -9)(j + -9) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (j + -9) equal to 8.94427191 and -8.94427191.Subproblem 1
j + -9 = 8.94427191 Simplifying j + -9 = 8.94427191 Reorder the terms: -9 + j = 8.94427191 Solving -9 + j = 8.94427191 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + j = 8.94427191 + 9 Combine like terms: -9 + 9 = 0 0 + j = 8.94427191 + 9 j = 8.94427191 + 9 Combine like terms: 8.94427191 + 9 = 17.94427191 j = 17.94427191 Simplifying j = 17.94427191Subproblem 2
j + -9 = -8.94427191 Simplifying j + -9 = -8.94427191 Reorder the terms: -9 + j = -8.94427191 Solving -9 + j = -8.94427191 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + j = -8.94427191 + 9 Combine like terms: -9 + 9 = 0 0 + j = -8.94427191 + 9 j = -8.94427191 + 9 Combine like terms: -8.94427191 + 9 = 0.05572809 j = 0.05572809 Simplifying j = 0.05572809Solution
The solution to the problem is based on the solutions from the subproblems. j = {17.94427191, 0.05572809}
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