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Simplifying -4j2 + -80j = -116 Reorder the terms: -80j + -4j2 = -116 Solving -80j + -4j2 = -116 Solving for variable 'j'. Reorder the terms: 116 + -80j + -4j2 = -116 + 116 Combine like terms: -116 + 116 = 0 116 + -80j + -4j2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(29 + -20j + -1j2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(29 + -20j + -1j2)' equal to zero and attempt to solve: Simplifying 29 + -20j + -1j2 = 0 Solving 29 + -20j + -1j2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -29 + 20j + j2 = 0 Move the constant term to the right: Add '29' to each side of the equation. -29 + 20j + 29 + j2 = 0 + 29 Reorder the terms: -29 + 29 + 20j + j2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 20j + j2 = 0 + 29 20j + j2 = 0 + 29 Combine like terms: 0 + 29 = 29 20j + j2 = 29 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 = 29 + 100 Reorder the terms: 100 + 20j + j2 = 29 + 100 Combine like terms: 29 + 100 = 129 100 + 20j + j2 = 129 Factor a perfect square on the left side: (j + 10)(j + 10) = 129 Calculate the square root of the right side: 11.357816692 Break this problem into two subproblems by setting (j + 10) equal to 11.357816692 and -11.357816692.Subproblem 1
j + 10 = 11.357816692 Simplifying j + 10 = 11.357816692 Reorder the terms: 10 + j = 11.357816692 Solving 10 + j = 11.357816692 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 = 11.357816692 + -10 Combine like terms: 10 + -10 = 0 0 + j = 11.357816692 + -10 j = 11.357816692 + -10 Combine like terms: 11.357816692 + -10 = 1.357816692 j = 1.357816692 Simplifying j = 1.357816692Subproblem 2
j + 10 = -11.357816692 Simplifying j + 10 = -11.357816692 Reorder the terms: 10 + j = -11.357816692 Solving 10 + j = -11.357816692 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 = -11.357816692 + -10 Combine like terms: 10 + -10 = 0 0 + j = -11.357816692 + -10 j = -11.357816692 + -10 Combine like terms: -11.357816692 + -10 = -21.357816692 j = -21.357816692 Simplifying j = -21.357816692Solution
The solution to the problem is based on the solutions from the subproblems. j = {1.357816692, -21.357816692}Solution
j = {1.357816692, -21.357816692}
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