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Simplifying j2 + -16j + -37 = 0 Reorder the terms: -37 + -16j + j2 = 0 Solving -37 + -16j + j2 = 0 Solving for variable 'j'. Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + -16j + 37 + j2 = 0 + 37 Reorder the terms: -37 + 37 + -16j + j2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -16j + j2 = 0 + 37 -16j + j2 = 0 + 37 Combine like terms: 0 + 37 = 37 -16j + j2 = 37 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 = 37 + 64 Reorder the terms: 64 + -16j + j2 = 37 + 64 Combine like terms: 37 + 64 = 101 64 + -16j + j2 = 101 Factor a perfect square on the left side: (j + -8)(j + -8) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (j + -8) equal to 10.049875621 and -10.049875621.Subproblem 1
j + -8 = 10.049875621 Simplifying j + -8 = 10.049875621 Reorder the terms: -8 + j = 10.049875621 Solving -8 + j = 10.049875621 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 = 10.049875621 + 8 Combine like terms: -8 + 8 = 0 0 + j = 10.049875621 + 8 j = 10.049875621 + 8 Combine like terms: 10.049875621 + 8 = 18.049875621 j = 18.049875621 Simplifying j = 18.049875621Subproblem 2
j + -8 = -10.049875621 Simplifying j + -8 = -10.049875621 Reorder the terms: -8 + j = -10.049875621 Solving -8 + j = -10.049875621 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 = -10.049875621 + 8 Combine like terms: -8 + 8 = 0 0 + j = -10.049875621 + 8 j = -10.049875621 + 8 Combine like terms: -10.049875621 + 8 = -2.049875621 j = -2.049875621 Simplifying j = -2.049875621Solution
The solution to the problem is based on the solutions from the subproblems. j = {18.049875621, -2.049875621}
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