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Simplifying j2 + 16j = 19 Reorder the terms: 16j + j2 = 19 Solving 16j + j2 = 19 Solving for variable 'j'. Reorder the terms: -19 + 16j + j2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + 16j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 16j + 19 + j2 = 0 + 19 Reorder the terms: -19 + 19 + 16j + j2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 16j + j2 = 0 + 19 16j + j2 = 0 + 19 Combine like terms: 0 + 19 = 19 16j + j2 = 19 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 = 19 + 64 Reorder the terms: 64 + 16j + j2 = 19 + 64 Combine like terms: 19 + 64 = 83 64 + 16j + j2 = 83 Factor a perfect square on the left side: (j + 8)(j + 8) = 83 Calculate the square root of the right side: 9.110433579 Break this problem into two subproblems by setting (j + 8) equal to 9.110433579 and -9.110433579.Subproblem 1
j + 8 = 9.110433579 Simplifying j + 8 = 9.110433579 Reorder the terms: 8 + j = 9.110433579 Solving 8 + j = 9.110433579 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 = 9.110433579 + -8 Combine like terms: 8 + -8 = 0 0 + j = 9.110433579 + -8 j = 9.110433579 + -8 Combine like terms: 9.110433579 + -8 = 1.110433579 j = 1.110433579 Simplifying j = 1.110433579Subproblem 2
j + 8 = -9.110433579 Simplifying j + 8 = -9.110433579 Reorder the terms: 8 + j = -9.110433579 Solving 8 + j = -9.110433579 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 = -9.110433579 + -8 Combine like terms: 8 + -8 = 0 0 + j = -9.110433579 + -8 j = -9.110433579 + -8 Combine like terms: -9.110433579 + -8 = -17.110433579 j = -17.110433579 Simplifying j = -17.110433579Solution
The solution to the problem is based on the solutions from the subproblems. j = {1.110433579, -17.110433579}
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