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Simplifying j2 + -42j + -144 = 0 Reorder the terms: -144 + -42j + j2 = 0 Solving -144 + -42j + j2 = 0 Solving for variable 'j'. Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + -42j + 144 + j2 = 0 + 144 Reorder the terms: -144 + 144 + -42j + j2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -42j + j2 = 0 + 144 -42j + j2 = 0 + 144 Combine like terms: 0 + 144 = 144 -42j + j2 = 144 The j term is -42j. Take half its coefficient (-21). Square it (441) and add it to both sides. Add '441' to each side of the equation. -42j + 441 + j2 = 144 + 441 Reorder the terms: 441 + -42j + j2 = 144 + 441 Combine like terms: 144 + 441 = 585 441 + -42j + j2 = 585 Factor a perfect square on the left side: (j + -21)(j + -21) = 585 Calculate the square root of the right side: 24.186773245 Break this problem into two subproblems by setting (j + -21) equal to 24.186773245 and -24.186773245.Subproblem 1
j + -21 = 24.186773245 Simplifying j + -21 = 24.186773245 Reorder the terms: -21 + j = 24.186773245 Solving -21 + j = 24.186773245 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + j = 24.186773245 + 21 Combine like terms: -21 + 21 = 0 0 + j = 24.186773245 + 21 j = 24.186773245 + 21 Combine like terms: 24.186773245 + 21 = 45.186773245 j = 45.186773245 Simplifying j = 45.186773245Subproblem 2
j + -21 = -24.186773245 Simplifying j + -21 = -24.186773245 Reorder the terms: -21 + j = -24.186773245 Solving -21 + j = -24.186773245 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + j = -24.186773245 + 21 Combine like terms: -21 + 21 = 0 0 + j = -24.186773245 + 21 j = -24.186773245 + 21 Combine like terms: -24.186773245 + 21 = -3.186773245 j = -3.186773245 Simplifying j = -3.186773245Solution
The solution to the problem is based on the solutions from the subproblems. j = {45.186773245, -3.186773245}
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