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Simplifying j2 + -28j + -3 = 0 Reorder the terms: -3 + -28j + j2 = 0 Solving -3 + -28j + j2 = 0 Solving for variable 'j'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -28j + 3 + j2 = 0 + 3 Reorder the terms: -3 + 3 + -28j + j2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -28j + j2 = 0 + 3 -28j + j2 = 0 + 3 Combine like terms: 0 + 3 = 3 -28j + j2 = 3 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 = 3 + 196 Reorder the terms: 196 + -28j + j2 = 3 + 196 Combine like terms: 3 + 196 = 199 196 + -28j + j2 = 199 Factor a perfect square on the left side: (j + -14)(j + -14) = 199 Calculate the square root of the right side: 14.10673598 Break this problem into two subproblems by setting (j + -14) equal to 14.10673598 and -14.10673598.Subproblem 1
j + -14 = 14.10673598 Simplifying j + -14 = 14.10673598 Reorder the terms: -14 + j = 14.10673598 Solving -14 + j = 14.10673598 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 = 14.10673598 + 14 Combine like terms: -14 + 14 = 0 0 + j = 14.10673598 + 14 j = 14.10673598 + 14 Combine like terms: 14.10673598 + 14 = 28.10673598 j = 28.10673598 Simplifying j = 28.10673598Subproblem 2
j + -14 = -14.10673598 Simplifying j + -14 = -14.10673598 Reorder the terms: -14 + j = -14.10673598 Solving -14 + j = -14.10673598 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 = -14.10673598 + 14 Combine like terms: -14 + 14 = 0 0 + j = -14.10673598 + 14 j = -14.10673598 + 14 Combine like terms: -14.10673598 + 14 = -0.10673598 j = -0.10673598 Simplifying j = -0.10673598Solution
The solution to the problem is based on the solutions from the subproblems. j = {28.10673598, -0.10673598}
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