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Simplifying -3j2 + -63j = -102 Reorder the terms: -63j + -3j2 = -102 Solving -63j + -3j2 = -102 Solving for variable 'j'. Reorder the terms: 102 + -63j + -3j2 = -102 + 102 Combine like terms: -102 + 102 = 0 102 + -63j + -3j2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(34 + -21j + -1j2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(34 + -21j + -1j2)' equal to zero and attempt to solve: Simplifying 34 + -21j + -1j2 = 0 Solving 34 + -21j + -1j2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -34 + 21j + j2 = 0 Move the constant term to the right: Add '34' to each side of the equation. -34 + 21j + 34 + j2 = 0 + 34 Reorder the terms: -34 + 34 + 21j + j2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 21j + j2 = 0 + 34 21j + j2 = 0 + 34 Combine like terms: 0 + 34 = 34 21j + j2 = 34 The j term is 21j. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21j + 110.25 + j2 = 34 + 110.25 Reorder the terms: 110.25 + 21j + j2 = 34 + 110.25 Combine like terms: 34 + 110.25 = 144.25 110.25 + 21j + j2 = 144.25 Factor a perfect square on the left side: (j + 10.5)(j + 10.5) = 144.25 Calculate the square root of the right side: 12.010412149 Break this problem into two subproblems by setting (j + 10.5) equal to 12.010412149 and -12.010412149.Subproblem 1
j + 10.5 = 12.010412149 Simplifying j + 10.5 = 12.010412149 Reorder the terms: 10.5 + j = 12.010412149 Solving 10.5 + j = 12.010412149 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + j = 12.010412149 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + j = 12.010412149 + -10.5 j = 12.010412149 + -10.5 Combine like terms: 12.010412149 + -10.5 = 1.510412149 j = 1.510412149 Simplifying j = 1.510412149Subproblem 2
j + 10.5 = -12.010412149 Simplifying j + 10.5 = -12.010412149 Reorder the terms: 10.5 + j = -12.010412149 Solving 10.5 + j = -12.010412149 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + j = -12.010412149 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + j = -12.010412149 + -10.5 j = -12.010412149 + -10.5 Combine like terms: -12.010412149 + -10.5 = -22.510412149 j = -22.510412149 Simplifying j = -22.510412149Solution
The solution to the problem is based on the solutions from the subproblems. j = {1.510412149, -22.510412149}Solution
j = {1.510412149, -22.510412149}
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