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Simplifying w2 + 4wj + -32j2 = 0 Reorder the terms: 4jw + -32j2 + w2 = 0 Solving 4jw + -32j2 + w2 = 0 Solving for variable 'j'. Factor a trinomial. (-8j + -1w)(4j + -1w) = 0Subproblem 1
Set the factor '(-8j + -1w)' equal to zero and attempt to solve: Simplifying -8j + -1w = 0 Solving -8j + -1w = 0 Move all terms containing j to the left, all other terms to the right. Add 'w' to each side of the equation. -8j + -1w + w = 0 + w Combine like terms: -1w + w = 0 -8j + 0 = 0 + w -8j = 0 + w Remove the zero: -8j = w Divide each side by '-8'. j = -0.125w Simplifying j = -0.125wSubproblem 2
Set the factor '(4j + -1w)' equal to zero and attempt to solve: Simplifying 4j + -1w = 0 Solving 4j + -1w = 0 Move all terms containing j to the left, all other terms to the right. Add 'w' to each side of the equation. 4j + -1w + w = 0 + w Combine like terms: -1w + w = 0 4j + 0 = 0 + w 4j = 0 + w Remove the zero: 4j = w Divide each side by '4'. j = 0.25w Simplifying j = 0.25wSolution
j = {-0.125w, 0.25w}
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