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Simplifying 8j2 + 94j + -24 = 0 Reorder the terms: -24 + 94j + 8j2 = 0 Solving -24 + 94j + 8j2 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 47j + 4j2) = 0 Factor a trinomial. 2((-12 + -1j)(1 + -4j)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + -1j)' equal to zero and attempt to solve: Simplifying -12 + -1j = 0 Solving -12 + -1j = 0 Move all terms containing j to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1j = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1j = 0 + 12 -1j = 0 + 12 Combine like terms: 0 + 12 = 12 -1j = 12 Divide each side by '-1'. j = -12 Simplifying j = -12Subproblem 2
Set the factor '(1 + -4j)' equal to zero and attempt to solve: Simplifying 1 + -4j = 0 Solving 1 + -4j = 0 Move all terms containing j to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4j = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4j = 0 + -1 -4j = 0 + -1 Combine like terms: 0 + -1 = -1 -4j = -1 Divide each side by '-4'. j = 0.25 Simplifying j = 0.25Solution
j = {-12, 0.25}
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