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Simplifying 2j2 + -4j + -30 = 0 Reorder the terms: -30 + -4j + 2j2 = 0 Solving -30 + -4j + 2j2 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -2j + j2) = 0 Factor a trinomial. 2((-3 + -1j)(5 + -1j)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -1j)' equal to zero and attempt to solve: Simplifying -3 + -1j = 0 Solving -3 + -1j = 0 Move all terms containing j to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1j = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1j = 0 + 3 -1j = 0 + 3 Combine like terms: 0 + 3 = 3 -1j = 3 Divide each side by '-1'. j = -3 Simplifying j = -3Subproblem 2
Set the factor '(5 + -1j)' equal to zero and attempt to solve: Simplifying 5 + -1j = 0 Solving 5 + -1j = 0 Move all terms containing j to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1j = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1j = 0 + -5 -1j = 0 + -5 Combine like terms: 0 + -5 = -5 -1j = -5 Divide each side by '-1'. j = 5 Simplifying j = 5Solution
j = {-3, 5}
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