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Simplifying j2 + 6j + -1 = 0 Reorder the terms: -1 + 6j + j2 = 0 Solving -1 + 6j + j2 = 0 Solving for variable 'j'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 6j + 1 + j2 = 0 + 1 Reorder the terms: -1 + 1 + 6j + j2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 6j + j2 = 0 + 1 6j + j2 = 0 + 1 Combine like terms: 0 + 1 = 1 6j + j2 = 1 The j term is 6j. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6j + 9 + j2 = 1 + 9 Reorder the terms: 9 + 6j + j2 = 1 + 9 Combine like terms: 1 + 9 = 10 9 + 6j + j2 = 10 Factor a perfect square on the left side: (j + 3)(j + 3) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (j + 3) equal to 3.16227766 and -3.16227766.Subproblem 1
j + 3 = 3.16227766 Simplifying j + 3 = 3.16227766 Reorder the terms: 3 + j = 3.16227766 Solving 3 + j = 3.16227766 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + j = 3.16227766 + -3 Combine like terms: 3 + -3 = 0 0 + j = 3.16227766 + -3 j = 3.16227766 + -3 Combine like terms: 3.16227766 + -3 = 0.16227766 j = 0.16227766 Simplifying j = 0.16227766Subproblem 2
j + 3 = -3.16227766 Simplifying j + 3 = -3.16227766 Reorder the terms: 3 + j = -3.16227766 Solving 3 + j = -3.16227766 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + j = -3.16227766 + -3 Combine like terms: 3 + -3 = 0 0 + j = -3.16227766 + -3 j = -3.16227766 + -3 Combine like terms: -3.16227766 + -3 = -6.16227766 j = -6.16227766 Simplifying j = -6.16227766Solution
The solution to the problem is based on the solutions from the subproblems. j = {0.16227766, -6.16227766}
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