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Simplifying 80 = -80j + -15j2 Solving 80 = -80j + -15j2 Solving for variable 'j'. Reorder the terms: 80 + 80j + 15j2 = -80j + 80j + -15j2 + 15j2 Combine like terms: -80j + 80j = 0 80 + 80j + 15j2 = 0 + -15j2 + 15j2 80 + 80j + 15j2 = -15j2 + 15j2 Combine like terms: -15j2 + 15j2 = 0 80 + 80j + 15j2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(16 + 16j + 3j2) = 0 Factor a trinomial. 5((4 + j)(4 + 3j)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(4 + j)' equal to zero and attempt to solve: Simplifying 4 + j = 0 Solving 4 + j = 0 Move all terms containing j to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + j = 0 + -4 Combine like terms: 4 + -4 = 0 0 + j = 0 + -4 j = 0 + -4 Combine like terms: 0 + -4 = -4 j = -4 Simplifying j = -4Subproblem 2
Set the factor '(4 + 3j)' equal to zero and attempt to solve: Simplifying 4 + 3j = 0 Solving 4 + 3j = 0 Move all terms containing j to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3j = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3j = 0 + -4 3j = 0 + -4 Combine like terms: 0 + -4 = -4 3j = -4 Divide each side by '3'. j = -1.333333333 Simplifying j = -1.333333333Solution
j = {-4, -1.333333333}
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