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Simplifying -3j2 + -90j = -69 Reorder the terms: -90j + -3j2 = -69 Solving -90j + -3j2 = -69 Solving for variable 'j'. Reorder the terms: 69 + -90j + -3j2 = -69 + 69 Combine like terms: -69 + 69 = 0 69 + -90j + -3j2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(23 + -30j + -1j2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(23 + -30j + -1j2)' equal to zero and attempt to solve: Simplifying 23 + -30j + -1j2 = 0 Solving 23 + -30j + -1j2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -23 + 30j + j2 = 0 Move the constant term to the right: Add '23' to each side of the equation. -23 + 30j + 23 + j2 = 0 + 23 Reorder the terms: -23 + 23 + 30j + j2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 30j + j2 = 0 + 23 30j + j2 = 0 + 23 Combine like terms: 0 + 23 = 23 30j + j2 = 23 The j term is 30j. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30j + 225 + j2 = 23 + 225 Reorder the terms: 225 + 30j + j2 = 23 + 225 Combine like terms: 23 + 225 = 248 225 + 30j + j2 = 248 Factor a perfect square on the left side: (j + 15)(j + 15) = 248 Calculate the square root of the right side: 15.748015748 Break this problem into two subproblems by setting (j + 15) equal to 15.748015748 and -15.748015748.Subproblem 1
j + 15 = 15.748015748 Simplifying j + 15 = 15.748015748 Reorder the terms: 15 + j = 15.748015748 Solving 15 + j = 15.748015748 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + j = 15.748015748 + -15 Combine like terms: 15 + -15 = 0 0 + j = 15.748015748 + -15 j = 15.748015748 + -15 Combine like terms: 15.748015748 + -15 = 0.748015748 j = 0.748015748 Simplifying j = 0.748015748Subproblem 2
j + 15 = -15.748015748 Simplifying j + 15 = -15.748015748 Reorder the terms: 15 + j = -15.748015748 Solving 15 + j = -15.748015748 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + j = -15.748015748 + -15 Combine like terms: 15 + -15 = 0 0 + j = -15.748015748 + -15 j = -15.748015748 + -15 Combine like terms: -15.748015748 + -15 = -30.748015748 j = -30.748015748 Simplifying j = -30.748015748Solution
The solution to the problem is based on the solutions from the subproblems. j = {0.748015748, -30.748015748}Solution
j = {0.748015748, -30.748015748}
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