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Simplifying -4j2 + -52j + -8 = 0 Reorder the terms: -8 + -52j + -4j2 = 0 Solving -8 + -52j + -4j2 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), '-4'. -4(2 + 13j + j2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(2 + 13j + j2)' equal to zero and attempt to solve: Simplifying 2 + 13j + j2 = 0 Solving 2 + 13j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 13j + -2 + j2 = 0 + -2 Reorder the terms: 2 + -2 + 13j + j2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 13j + j2 = 0 + -2 13j + j2 = 0 + -2 Combine like terms: 0 + -2 = -2 13j + j2 = -2 The j term is 13j. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13j + 42.25 + j2 = -2 + 42.25 Reorder the terms: 42.25 + 13j + j2 = -2 + 42.25 Combine like terms: -2 + 42.25 = 40.25 42.25 + 13j + j2 = 40.25 Factor a perfect square on the left side: (j + 6.5)(j + 6.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (j + 6.5) equal to 6.34428877 and -6.34428877.Subproblem 1
j + 6.5 = 6.34428877 Simplifying j + 6.5 = 6.34428877 Reorder the terms: 6.5 + j = 6.34428877 Solving 6.5 + j = 6.34428877 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + j = 6.34428877 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + j = 6.34428877 + -6.5 j = 6.34428877 + -6.5 Combine like terms: 6.34428877 + -6.5 = -0.15571123 j = -0.15571123 Simplifying j = -0.15571123Subproblem 2
j + 6.5 = -6.34428877 Simplifying j + 6.5 = -6.34428877 Reorder the terms: 6.5 + j = -6.34428877 Solving 6.5 + j = -6.34428877 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + j = -6.34428877 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + j = -6.34428877 + -6.5 j = -6.34428877 + -6.5 Combine like terms: -6.34428877 + -6.5 = -12.84428877 j = -12.84428877 Simplifying j = -12.84428877Solution
The solution to the problem is based on the solutions from the subproblems. j = {-0.15571123, -12.84428877}Solution
j = {-0.15571123, -12.84428877}
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