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Simplifying 5j2 + 5j + -8 = 0 Reorder the terms: -8 + 5j + 5j2 = 0 Solving -8 + 5j + 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'. -1.6 + j + j2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + j + 1.6 + j2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + j + j2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + j + j2 = 0 + 1.6 j + j2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 j + j2 = 1.6 The j term is j. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + j2 = 1.6 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + j2 = 1.6 + 0.25 Combine like terms: 1.6 + 0.25 = 1.85 1.25 + j2 = 1.85 Factor a perfect square on the left side: (j + 0.5)(j + 0.5) = 1.85 Calculate the square root of the right side: 1.360147051 Break this problem into two subproblems by setting (j + 0.5) equal to 1.360147051 and -1.360147051.Subproblem 1
j + 0.5 = 1.360147051 Simplifying j + 0.5 = 1.360147051 Reorder the terms: 0.5 + j = 1.360147051 Solving 0.5 + j = 1.360147051 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + j = 1.360147051 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + j = 1.360147051 + -0.5 j = 1.360147051 + -0.5 Combine like terms: 1.360147051 + -0.5 = 0.860147051 j = 0.860147051 Simplifying j = 0.860147051Subproblem 2
j + 0.5 = -1.360147051 Simplifying j + 0.5 = -1.360147051 Reorder the terms: 0.5 + j = -1.360147051 Solving 0.5 + j = -1.360147051 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + j = -1.360147051 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + j = -1.360147051 + -0.5 j = -1.360147051 + -0.5 Combine like terms: -1.360147051 + -0.5 = -1.860147051 j = -1.860147051 Simplifying j = -1.860147051Solution
The solution to the problem is based on the solutions from the subproblems. j = {0.860147051, -1.860147051}
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