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Simplifying j2 + 16j = 43 Reorder the terms: 16j + j2 = 43 Solving 16j + j2 = 43 Solving for variable 'j'. Reorder the terms: -43 + 16j + j2 = 43 + -43 Combine like terms: 43 + -43 = 0 -43 + 16j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + 16j + 43 + j2 = 0 + 43 Reorder the terms: -43 + 43 + 16j + j2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 16j + j2 = 0 + 43 16j + j2 = 0 + 43 Combine like terms: 0 + 43 = 43 16j + j2 = 43 The j term is 16j. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16j + 64 + j2 = 43 + 64 Reorder the terms: 64 + 16j + j2 = 43 + 64 Combine like terms: 43 + 64 = 107 64 + 16j + j2 = 107 Factor a perfect square on the left side: (j + 8)(j + 8) = 107 Calculate the square root of the right side: 10.344080433 Break this problem into two subproblems by setting (j + 8) equal to 10.344080433 and -10.344080433.Subproblem 1
j + 8 = 10.344080433 Simplifying j + 8 = 10.344080433 Reorder the terms: 8 + j = 10.344080433 Solving 8 + j = 10.344080433 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + j = 10.344080433 + -8 Combine like terms: 8 + -8 = 0 0 + j = 10.344080433 + -8 j = 10.344080433 + -8 Combine like terms: 10.344080433 + -8 = 2.344080433 j = 2.344080433 Simplifying j = 2.344080433Subproblem 2
j + 8 = -10.344080433 Simplifying j + 8 = -10.344080433 Reorder the terms: 8 + j = -10.344080433 Solving 8 + j = -10.344080433 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + j = -10.344080433 + -8 Combine like terms: 8 + -8 = 0 0 + j = -10.344080433 + -8 j = -10.344080433 + -8 Combine like terms: -10.344080433 + -8 = -18.344080433 j = -18.344080433 Simplifying j = -18.344080433Solution
The solution to the problem is based on the solutions from the subproblems. j = {2.344080433, -18.344080433}
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