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Simplifying j2 + -12j + 23 = 0 Reorder the terms: 23 + -12j + j2 = 0 Solving 23 + -12j + 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 + -12j + -23 + j2 = 0 + -23 Reorder the terms: 23 + -23 + -12j + j2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -12j + j2 = 0 + -23 -12j + j2 = 0 + -23 Combine like terms: 0 + -23 = -23 -12j + j2 = -23 The j term is -12j. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12j + 36 + j2 = -23 + 36 Reorder the terms: 36 + -12j + j2 = -23 + 36 Combine like terms: -23 + 36 = 13 36 + -12j + j2 = 13 Factor a perfect square on the left side: (j + -6)(j + -6) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (j + -6) equal to 3.605551275 and -3.605551275.Subproblem 1
j + -6 = 3.605551275 Simplifying j + -6 = 3.605551275 Reorder the terms: -6 + j = 3.605551275 Solving -6 + j = 3.605551275 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + j = 3.605551275 + 6 Combine like terms: -6 + 6 = 0 0 + j = 3.605551275 + 6 j = 3.605551275 + 6 Combine like terms: 3.605551275 + 6 = 9.605551275 j = 9.605551275 Simplifying j = 9.605551275Subproblem 2
j + -6 = -3.605551275 Simplifying j + -6 = -3.605551275 Reorder the terms: -6 + j = -3.605551275 Solving -6 + j = -3.605551275 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + j = -3.605551275 + 6 Combine like terms: -6 + 6 = 0 0 + j = -3.605551275 + 6 j = -3.605551275 + 6 Combine like terms: -3.605551275 + 6 = 2.394448725 j = 2.394448725 Simplifying j = 2.394448725Solution
The solution to the problem is based on the solutions from the subproblems. j = {9.605551275, 2.394448725}
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