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Simplifying j2 + -28j = -29 Reorder the terms: -28j + j2 = -29 Solving -28j + j2 = -29 Solving for variable 'j'. Reorder the terms: 29 + -28j + j2 = -29 + 29 Combine like terms: -29 + 29 = 0 29 + -28j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + -28j + -29 + j2 = 0 + -29 Reorder the terms: 29 + -29 + -28j + j2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -28j + j2 = 0 + -29 -28j + j2 = 0 + -29 Combine like terms: 0 + -29 = -29 -28j + j2 = -29 The j term is -28j. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28j + 196 + j2 = -29 + 196 Reorder the terms: 196 + -28j + j2 = -29 + 196 Combine like terms: -29 + 196 = 167 196 + -28j + j2 = 167 Factor a perfect square on the left side: (j + -14)(j + -14) = 167 Calculate the square root of the right side: 12.922847983 Break this problem into two subproblems by setting (j + -14) equal to 12.922847983 and -12.922847983.Subproblem 1
j + -14 = 12.922847983 Simplifying j + -14 = 12.922847983 Reorder the terms: -14 + j = 12.922847983 Solving -14 + j = 12.922847983 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + j = 12.922847983 + 14 Combine like terms: -14 + 14 = 0 0 + j = 12.922847983 + 14 j = 12.922847983 + 14 Combine like terms: 12.922847983 + 14 = 26.922847983 j = 26.922847983 Simplifying j = 26.922847983Subproblem 2
j + -14 = -12.922847983 Simplifying j + -14 = -12.922847983 Reorder the terms: -14 + j = -12.922847983 Solving -14 + j = -12.922847983 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + j = -12.922847983 + 14 Combine like terms: -14 + 14 = 0 0 + j = -12.922847983 + 14 j = -12.922847983 + 14 Combine like terms: -12.922847983 + 14 = 1.077152017 j = 1.077152017 Simplifying j = 1.077152017Solution
The solution to the problem is based on the solutions from the subproblems. j = {26.922847983, 1.077152017}
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