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Simplifying j2 + 6j = 5 Reorder the terms: 6j + j2 = 5 Solving 6j + j2 = 5 Solving for variable 'j'. Reorder the terms: -5 + 6j + j2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 6j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 6j + 5 + j2 = 0 + 5 Reorder the terms: -5 + 5 + 6j + j2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 6j + j2 = 0 + 5 6j + j2 = 0 + 5 Combine like terms: 0 + 5 = 5 6j + j2 = 5 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 = 5 + 9 Reorder the terms: 9 + 6j + j2 = 5 + 9 Combine like terms: 5 + 9 = 14 9 + 6j + j2 = 14 Factor a perfect square on the left side: (j + 3)(j + 3) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (j + 3) equal to 3.741657387 and -3.741657387.Subproblem 1
j + 3 = 3.741657387 Simplifying j + 3 = 3.741657387 Reorder the terms: 3 + j = 3.741657387 Solving 3 + j = 3.741657387 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 = 3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + j = 3.741657387 + -3 j = 3.741657387 + -3 Combine like terms: 3.741657387 + -3 = 0.741657387 j = 0.741657387 Simplifying j = 0.741657387Subproblem 2
j + 3 = -3.741657387 Simplifying j + 3 = -3.741657387 Reorder the terms: 3 + j = -3.741657387 Solving 3 + j = -3.741657387 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 = -3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + j = -3.741657387 + -3 j = -3.741657387 + -3 Combine like terms: -3.741657387 + -3 = -6.741657387 j = -6.741657387 Simplifying j = -6.741657387Solution
The solution to the problem is based on the solutions from the subproblems. j = {0.741657387, -6.741657387}
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