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Simplifying 5j2 + 8j + -3 = 0 Reorder the terms: -3 + 8j + 5j2 = 0 Solving -3 + 8j + 5j2 = 0 Solving for variable 'j'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + 1.6j + j2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 1.6j + 0.6 + j2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 1.6j + j2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 1.6j + j2 = 0 + 0.6 1.6j + j2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 1.6j + j2 = 0.6 The j term is 1.6j. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6j + 0.64 + j2 = 0.6 + 0.64 Reorder the terms: 0.64 + 1.6j + j2 = 0.6 + 0.64 Combine like terms: 0.6 + 0.64 = 1.24 0.64 + 1.6j + j2 = 1.24 Factor a perfect square on the left side: (j + 0.8)(j + 0.8) = 1.24 Calculate the square root of the right side: 1.113552873 Break this problem into two subproblems by setting (j + 0.8) equal to 1.113552873 and -1.113552873.Subproblem 1
j + 0.8 = 1.113552873 Simplifying j + 0.8 = 1.113552873 Reorder the terms: 0.8 + j = 1.113552873 Solving 0.8 + j = 1.113552873 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + j = 1.113552873 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + j = 1.113552873 + -0.8 j = 1.113552873 + -0.8 Combine like terms: 1.113552873 + -0.8 = 0.313552873 j = 0.313552873 Simplifying j = 0.313552873Subproblem 2
j + 0.8 = -1.113552873 Simplifying j + 0.8 = -1.113552873 Reorder the terms: 0.8 + j = -1.113552873 Solving 0.8 + j = -1.113552873 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + j = -1.113552873 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + j = -1.113552873 + -0.8 j = -1.113552873 + -0.8 Combine like terms: -1.113552873 + -0.8 = -1.913552873 j = -1.913552873 Simplifying j = -1.913552873Solution
The solution to the problem is based on the solutions from the subproblems. j = {0.313552873, -1.913552873}
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