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Simplifying -3j2 + 54j = 15 Reorder the terms: 54j + -3j2 = 15 Solving 54j + -3j2 = 15 Solving for variable 'j'. Reorder the terms: -15 + 54j + -3j2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 54j + -3j2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 18j + -1j2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + 18j + -1j2)' equal to zero and attempt to solve: Simplifying -5 + 18j + -1j2 = 0 Solving -5 + 18j + -1j2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5 + -18j + j2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -18j + -5 + j2 = 0 + -5 Reorder the terms: 5 + -5 + -18j + j2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -18j + j2 = 0 + -5 -18j + j2 = 0 + -5 Combine like terms: 0 + -5 = -5 -18j + j2 = -5 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 = -5 + 81 Reorder the terms: 81 + -18j + j2 = -5 + 81 Combine like terms: -5 + 81 = 76 81 + -18j + j2 = 76 Factor a perfect square on the left side: (j + -9)(j + -9) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (j + -9) equal to 8.717797887 and -8.717797887.Subproblem 1
j + -9 = 8.717797887 Simplifying j + -9 = 8.717797887 Reorder the terms: -9 + j = 8.717797887 Solving -9 + j = 8.717797887 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 = 8.717797887 + 9 Combine like terms: -9 + 9 = 0 0 + j = 8.717797887 + 9 j = 8.717797887 + 9 Combine like terms: 8.717797887 + 9 = 17.717797887 j = 17.717797887 Simplifying j = 17.717797887Subproblem 2
j + -9 = -8.717797887 Simplifying j + -9 = -8.717797887 Reorder the terms: -9 + j = -8.717797887 Solving -9 + j = -8.717797887 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 = -8.717797887 + 9 Combine like terms: -9 + 9 = 0 0 + j = -8.717797887 + 9 j = -8.717797887 + 9 Combine like terms: -8.717797887 + 9 = 0.282202113 j = 0.282202113 Simplifying j = 0.282202113Solution
The solution to the problem is based on the solutions from the subproblems. j = {17.717797887, 0.282202113}Solution
j = {17.717797887, 0.282202113}
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