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Simplifying j2 + -22j + 45 = 0 Reorder the terms: 45 + -22j + j2 = 0 Solving 45 + -22j + j2 = 0 Solving for variable 'j'. Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + -22j + -45 + j2 = 0 + -45 Reorder the terms: 45 + -45 + -22j + j2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -22j + j2 = 0 + -45 -22j + j2 = 0 + -45 Combine like terms: 0 + -45 = -45 -22j + j2 = -45 The j term is -22j. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22j + 121 + j2 = -45 + 121 Reorder the terms: 121 + -22j + j2 = -45 + 121 Combine like terms: -45 + 121 = 76 121 + -22j + j2 = 76 Factor a perfect square on the left side: (j + -11)(j + -11) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (j + -11) equal to 8.717797887 and -8.717797887.Subproblem 1
j + -11 = 8.717797887 Simplifying j + -11 = 8.717797887 Reorder the terms: -11 + j = 8.717797887 Solving -11 + j = 8.717797887 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + j = 8.717797887 + 11 Combine like terms: -11 + 11 = 0 0 + j = 8.717797887 + 11 j = 8.717797887 + 11 Combine like terms: 8.717797887 + 11 = 19.717797887 j = 19.717797887 Simplifying j = 19.717797887Subproblem 2
j + -11 = -8.717797887 Simplifying j + -11 = -8.717797887 Reorder the terms: -11 + j = -8.717797887 Solving -11 + j = -8.717797887 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + j = -8.717797887 + 11 Combine like terms: -11 + 11 = 0 0 + j = -8.717797887 + 11 j = -8.717797887 + 11 Combine like terms: -8.717797887 + 11 = 2.282202113 j = 2.282202113 Simplifying j = 2.282202113Solution
The solution to the problem is based on the solutions from the subproblems. j = {19.717797887, 2.282202113}
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