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Simplifying j2 + 2j = 13 Reorder the terms: 2j + j2 = 13 Solving 2j + j2 = 13 Solving for variable 'j'. Reorder the terms: -13 + 2j + j2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 2j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 2j + 13 + j2 = 0 + 13 Reorder the terms: -13 + 13 + 2j + j2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 2j + j2 = 0 + 13 2j + j2 = 0 + 13 Combine like terms: 0 + 13 = 13 2j + j2 = 13 The j term is 2j. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2j + 1 + j2 = 13 + 1 Reorder the terms: 1 + 2j + j2 = 13 + 1 Combine like terms: 13 + 1 = 14 1 + 2j + j2 = 14 Factor a perfect square on the left side: (j + 1)(j + 1) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (j + 1) equal to 3.741657387 and -3.741657387.Subproblem 1
j + 1 = 3.741657387 Simplifying j + 1 = 3.741657387 Reorder the terms: 1 + j = 3.741657387 Solving 1 + j = 3.741657387 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + j = 3.741657387 + -1 Combine like terms: 1 + -1 = 0 0 + j = 3.741657387 + -1 j = 3.741657387 + -1 Combine like terms: 3.741657387 + -1 = 2.741657387 j = 2.741657387 Simplifying j = 2.741657387Subproblem 2
j + 1 = -3.741657387 Simplifying j + 1 = -3.741657387 Reorder the terms: 1 + j = -3.741657387 Solving 1 + j = -3.741657387 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + j = -3.741657387 + -1 Combine like terms: 1 + -1 = 0 0 + j = -3.741657387 + -1 j = -3.741657387 + -1 Combine like terms: -3.741657387 + -1 = -4.741657387 j = -4.741657387 Simplifying j = -4.741657387Solution
The solution to the problem is based on the solutions from the subproblems. j = {2.741657387, -4.741657387}
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