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Simplifying 15j2 + -10j + -80 = 0 Reorder the terms: -80 + -10j + 15j2 = 0 Solving -80 + -10j + 15j2 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), '5'. 5(-16 + -2j + 3j2) = 0 Factor a trinomial. 5((-2 + -1j)(8 + -3j)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + -1j)' equal to zero and attempt to solve: Simplifying -2 + -1j = 0 Solving -2 + -1j = 0 Move all terms containing j to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1j = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1j = 0 + 2 -1j = 0 + 2 Combine like terms: 0 + 2 = 2 -1j = 2 Divide each side by '-1'. j = -2 Simplifying j = -2Subproblem 2
Set the factor '(8 + -3j)' equal to zero and attempt to solve: Simplifying 8 + -3j = 0 Solving 8 + -3j = 0 Move all terms containing j to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3j = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3j = 0 + -8 -3j = 0 + -8 Combine like terms: 0 + -8 = -8 -3j = -8 Divide each side by '-3'. j = 2.666666667 Simplifying j = 2.666666667Solution
j = {-2, 2.666666667}
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