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Simplifying 12j2 + 86j + 14 = 0 Reorder the terms: 14 + 86j + 12j2 = 0 Solving 14 + 86j + 12j2 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 43j + 6j2) = 0 Factor a trinomial. 2((7 + j)(1 + 6j)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + j)' equal to zero and attempt to solve: Simplifying 7 + j = 0 Solving 7 + j = 0 Move all terms containing j to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + j = 0 + -7 Combine like terms: 7 + -7 = 0 0 + j = 0 + -7 j = 0 + -7 Combine like terms: 0 + -7 = -7 j = -7 Simplifying j = -7Subproblem 2
Set the factor '(1 + 6j)' equal to zero and attempt to solve: Simplifying 1 + 6j = 0 Solving 1 + 6j = 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 + 6j = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6j = 0 + -1 6j = 0 + -1 Combine like terms: 0 + -1 = -1 6j = -1 Divide each side by '6'. j = -0.1666666667 Simplifying j = -0.1666666667Solution
j = {-7, -0.1666666667}
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