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Simplifying 8j2 + -5j + -8 = 0 Reorder the terms: -8 + -5j + 8j2 = 0 Solving -8 + -5j + 8j2 = 0 Solving for variable 'j'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1 + -0.625j + j2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.625j + 1 + j2 = 0 + 1 Reorder the terms: -1 + 1 + -0.625j + j2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.625j + j2 = 0 + 1 -0.625j + j2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.625j + j2 = 1 The j term is -0.625j. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625j + 0.09765625 + j2 = 1 + 0.09765625 Reorder the terms: 0.09765625 + -0.625j + j2 = 1 + 0.09765625 Combine like terms: 1 + 0.09765625 = 1.09765625 0.09765625 + -0.625j + j2 = 1.09765625 Factor a perfect square on the left side: (j + -0.3125)(j + -0.3125) = 1.09765625 Calculate the square root of the right side: 1.047690913 Break this problem into two subproblems by setting (j + -0.3125) equal to 1.047690913 and -1.047690913.Subproblem 1
j + -0.3125 = 1.047690913 Simplifying j + -0.3125 = 1.047690913 Reorder the terms: -0.3125 + j = 1.047690913 Solving -0.3125 + j = 1.047690913 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + j = 1.047690913 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + j = 1.047690913 + 0.3125 j = 1.047690913 + 0.3125 Combine like terms: 1.047690913 + 0.3125 = 1.360190913 j = 1.360190913 Simplifying j = 1.360190913Subproblem 2
j + -0.3125 = -1.047690913 Simplifying j + -0.3125 = -1.047690913 Reorder the terms: -0.3125 + j = -1.047690913 Solving -0.3125 + j = -1.047690913 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + j = -1.047690913 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + j = -1.047690913 + 0.3125 j = -1.047690913 + 0.3125 Combine like terms: -1.047690913 + 0.3125 = -0.735190913 j = -0.735190913 Simplifying j = -0.735190913Solution
The solution to the problem is based on the solutions from the subproblems. j = {1.360190913, -0.735190913}
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