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Simplifying j2 + -2j = 19 Reorder the terms: -2j + j2 = 19 Solving -2j + j2 = 19 Solving for variable 'j'. Reorder the terms: -19 + -2j + j2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + -2j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -2j + 19 + j2 = 0 + 19 Reorder the terms: -19 + 19 + -2j + j2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -2j + j2 = 0 + 19 -2j + j2 = 0 + 19 Combine like terms: 0 + 19 = 19 -2j + j2 = 19 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 = 19 + 1 Reorder the terms: 1 + -2j + j2 = 19 + 1 Combine like terms: 19 + 1 = 20 1 + -2j + j2 = 20 Factor a perfect square on the left side: (j + -1)(j + -1) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (j + -1) equal to 4.472135955 and -4.472135955.Subproblem 1
j + -1 = 4.472135955 Simplifying j + -1 = 4.472135955 Reorder the terms: -1 + j = 4.472135955 Solving -1 + j = 4.472135955 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 = 4.472135955 + 1 Combine like terms: -1 + 1 = 0 0 + j = 4.472135955 + 1 j = 4.472135955 + 1 Combine like terms: 4.472135955 + 1 = 5.472135955 j = 5.472135955 Simplifying j = 5.472135955Subproblem 2
j + -1 = -4.472135955 Simplifying j + -1 = -4.472135955 Reorder the terms: -1 + j = -4.472135955 Solving -1 + j = -4.472135955 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 = -4.472135955 + 1 Combine like terms: -1 + 1 = 0 0 + j = -4.472135955 + 1 j = -4.472135955 + 1 Combine like terms: -4.472135955 + 1 = -3.472135955 j = -3.472135955 Simplifying j = -3.472135955Solution
The solution to the problem is based on the solutions from the subproblems. j = {5.472135955, -3.472135955}
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