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Simplifying j2 + 20j + 43 = 0 Reorder the terms: 43 + 20j + j2 = 0 Solving 43 + 20j + j2 = 0 Solving for variable 'j'. Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + 20j + -43 + j2 = 0 + -43 Reorder the terms: 43 + -43 + 20j + j2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + 20j + j2 = 0 + -43 20j + j2 = 0 + -43 Combine like terms: 0 + -43 = -43 20j + j2 = -43 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 = -43 + 100 Reorder the terms: 100 + 20j + j2 = -43 + 100 Combine like terms: -43 + 100 = 57 100 + 20j + j2 = 57 Factor a perfect square on the left side: (j + 10)(j + 10) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (j + 10) equal to 7.549834435 and -7.549834435.Subproblem 1
j + 10 = 7.549834435 Simplifying j + 10 = 7.549834435 Reorder the terms: 10 + j = 7.549834435 Solving 10 + j = 7.549834435 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 = 7.549834435 + -10 Combine like terms: 10 + -10 = 0 0 + j = 7.549834435 + -10 j = 7.549834435 + -10 Combine like terms: 7.549834435 + -10 = -2.450165565 j = -2.450165565 Simplifying j = -2.450165565Subproblem 2
j + 10 = -7.549834435 Simplifying j + 10 = -7.549834435 Reorder the terms: 10 + j = -7.549834435 Solving 10 + j = -7.549834435 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 = -7.549834435 + -10 Combine like terms: 10 + -10 = 0 0 + j = -7.549834435 + -10 j = -7.549834435 + -10 Combine like terms: -7.549834435 + -10 = -17.549834435 j = -17.549834435 Simplifying j = -17.549834435Solution
The solution to the problem is based on the solutions from the subproblems. j = {-2.450165565, -17.549834435}
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