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Simplifying 12j2 + 40j = 7 Reorder the terms: 40j + 12j2 = 7 Solving 40j + 12j2 = 7 Solving for variable 'j'. Reorder the terms: -7 + 40j + 12j2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 40j + 12j2 = 0 Factor a trinomial. (-7 + -2j)(1 + -6j) = 0Subproblem 1
Set the factor '(-7 + -2j)' equal to zero and attempt to solve: Simplifying -7 + -2j = 0 Solving -7 + -2j = 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 + -2j = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2j = 0 + 7 -2j = 0 + 7 Combine like terms: 0 + 7 = 7 -2j = 7 Divide each side by '-2'. j = -3.5 Simplifying j = -3.5Subproblem 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 = {-3.5, 0.1666666667}
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