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Simplifying j2 + 2j = 29 Reorder the terms: 2j + j2 = 29 Solving 2j + j2 = 29 Solving for variable 'j'. Reorder the terms: -29 + 2j + j2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + 2j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 2j + 29 + j2 = 0 + 29 Reorder the terms: -29 + 29 + 2j + j2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 2j + j2 = 0 + 29 2j + j2 = 0 + 29 Combine like terms: 0 + 29 = 29 2j + j2 = 29 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 = 29 + 1 Reorder the terms: 1 + 2j + j2 = 29 + 1 Combine like terms: 29 + 1 = 30 1 + 2j + j2 = 30 Factor a perfect square on the left side: (j + 1)(j + 1) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (j + 1) equal to 5.477225575 and -5.477225575.Subproblem 1
j + 1 = 5.477225575 Simplifying j + 1 = 5.477225575 Reorder the terms: 1 + j = 5.477225575 Solving 1 + j = 5.477225575 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 = 5.477225575 + -1 Combine like terms: 1 + -1 = 0 0 + j = 5.477225575 + -1 j = 5.477225575 + -1 Combine like terms: 5.477225575 + -1 = 4.477225575 j = 4.477225575 Simplifying j = 4.477225575Subproblem 2
j + 1 = -5.477225575 Simplifying j + 1 = -5.477225575 Reorder the terms: 1 + j = -5.477225575 Solving 1 + j = -5.477225575 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 = -5.477225575 + -1 Combine like terms: 1 + -1 = 0 0 + j = -5.477225575 + -1 j = -5.477225575 + -1 Combine like terms: -5.477225575 + -1 = -6.477225575 j = -6.477225575 Simplifying j = -6.477225575Solution
The solution to the problem is based on the solutions from the subproblems. j = {4.477225575, -6.477225575}
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