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Simplifying -1j2 + -9j + -7 = 0 Reorder the terms: -7 + -9j + -1j2 = 0 Solving -7 + -9j + -1j2 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 9j + j2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 9j + j2)' equal to zero and attempt to solve: Simplifying 7 + 9j + j2 = 0 Solving 7 + 9j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 9j + -7 + j2 = 0 + -7 Reorder the terms: 7 + -7 + 9j + j2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 9j + j2 = 0 + -7 9j + j2 = 0 + -7 Combine like terms: 0 + -7 = -7 9j + j2 = -7 The j term is 9j. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9j + 20.25 + j2 = -7 + 20.25 Reorder the terms: 20.25 + 9j + j2 = -7 + 20.25 Combine like terms: -7 + 20.25 = 13.25 20.25 + 9j + j2 = 13.25 Factor a perfect square on the left side: (j + 4.5)(j + 4.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (j + 4.5) equal to 3.640054945 and -3.640054945.Subproblem 1
j + 4.5 = 3.640054945 Simplifying j + 4.5 = 3.640054945 Reorder the terms: 4.5 + j = 3.640054945 Solving 4.5 + j = 3.640054945 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + j = 3.640054945 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + j = 3.640054945 + -4.5 j = 3.640054945 + -4.5 Combine like terms: 3.640054945 + -4.5 = -0.859945055 j = -0.859945055 Simplifying j = -0.859945055Subproblem 2
j + 4.5 = -3.640054945 Simplifying j + 4.5 = -3.640054945 Reorder the terms: 4.5 + j = -3.640054945 Solving 4.5 + j = -3.640054945 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + j = -3.640054945 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + j = -3.640054945 + -4.5 j = -3.640054945 + -4.5 Combine like terms: -3.640054945 + -4.5 = -8.140054945 j = -8.140054945 Simplifying j = -8.140054945Solution
The solution to the problem is based on the solutions from the subproblems. j = {-0.859945055, -8.140054945}Solution
j = {-0.859945055, -8.140054945}
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