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Simplifying j2 + -20j + -36 = 0 Reorder the terms: -36 + -20j + j2 = 0 Solving -36 + -20j + j2 = 0 Solving for variable 'j'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -20j + 36 + j2 = 0 + 36 Reorder the terms: -36 + 36 + -20j + j2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -20j + j2 = 0 + 36 -20j + j2 = 0 + 36 Combine like terms: 0 + 36 = 36 -20j + j2 = 36 The j term is -20j. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20j + 100 + j2 = 36 + 100 Reorder the terms: 100 + -20j + j2 = 36 + 100 Combine like terms: 36 + 100 = 136 100 + -20j + j2 = 136 Factor a perfect square on the left side: (j + -10)(j + -10) = 136 Calculate the square root of the right side: 11.66190379 Break this problem into two subproblems by setting (j + -10) equal to 11.66190379 and -11.66190379.Subproblem 1
j + -10 = 11.66190379 Simplifying j + -10 = 11.66190379 Reorder the terms: -10 + j = 11.66190379 Solving -10 + j = 11.66190379 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + j = 11.66190379 + 10 Combine like terms: -10 + 10 = 0 0 + j = 11.66190379 + 10 j = 11.66190379 + 10 Combine like terms: 11.66190379 + 10 = 21.66190379 j = 21.66190379 Simplifying j = 21.66190379Subproblem 2
j + -10 = -11.66190379 Simplifying j + -10 = -11.66190379 Reorder the terms: -10 + j = -11.66190379 Solving -10 + j = -11.66190379 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + j = -11.66190379 + 10 Combine like terms: -10 + 10 = 0 0 + j = -11.66190379 + 10 j = -11.66190379 + 10 Combine like terms: -11.66190379 + 10 = -1.66190379 j = -1.66190379 Simplifying j = -1.66190379Solution
The solution to the problem is based on the solutions from the subproblems. j = {21.66190379, -1.66190379}
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