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Simplifying j2 + -18j + -23 = 0 Reorder the terms: -23 + -18j + j2 = 0 Solving -23 + -18j + j2 = 0 Solving for variable 'j'. Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -18j + 23 + j2 = 0 + 23 Reorder the terms: -23 + 23 + -18j + j2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -18j + j2 = 0 + 23 -18j + j2 = 0 + 23 Combine like terms: 0 + 23 = 23 -18j + j2 = 23 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 = 23 + 81 Reorder the terms: 81 + -18j + j2 = 23 + 81 Combine like terms: 23 + 81 = 104 81 + -18j + j2 = 104 Factor a perfect square on the left side: (j + -9)(j + -9) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (j + -9) equal to 10.198039027 and -10.198039027.Subproblem 1
j + -9 = 10.198039027 Simplifying j + -9 = 10.198039027 Reorder the terms: -9 + j = 10.198039027 Solving -9 + j = 10.198039027 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 = 10.198039027 + 9 Combine like terms: -9 + 9 = 0 0 + j = 10.198039027 + 9 j = 10.198039027 + 9 Combine like terms: 10.198039027 + 9 = 19.198039027 j = 19.198039027 Simplifying j = 19.198039027Subproblem 2
j + -9 = -10.198039027 Simplifying j + -9 = -10.198039027 Reorder the terms: -9 + j = -10.198039027 Solving -9 + j = -10.198039027 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 = -10.198039027 + 9 Combine like terms: -9 + 9 = 0 0 + j = -10.198039027 + 9 j = -10.198039027 + 9 Combine like terms: -10.198039027 + 9 = -1.198039027 j = -1.198039027 Simplifying j = -1.198039027Solution
The solution to the problem is based on the solutions from the subproblems. j = {19.198039027, -1.198039027}
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