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Simplifying w2 + 4wg + -32g2 = 0 Reorder the terms: 4gw + -32g2 + w2 = 0 Solving 4gw + -32g2 + w2 = 0 Solving for variable 'g'. Factor a trinomial. (-8g + -1w)(4g + -1w) = 0Subproblem 1
Set the factor '(-8g + -1w)' equal to zero and attempt to solve: Simplifying -8g + -1w = 0 Solving -8g + -1w = 0 Move all terms containing g to the left, all other terms to the right. Add 'w' to each side of the equation. -8g + -1w + w = 0 + w Combine like terms: -1w + w = 0 -8g + 0 = 0 + w -8g = 0 + w Remove the zero: -8g = w Divide each side by '-8'. g = -0.125w Simplifying g = -0.125wSubproblem 2
Set the factor '(4g + -1w)' equal to zero and attempt to solve: Simplifying 4g + -1w = 0 Solving 4g + -1w = 0 Move all terms containing g to the left, all other terms to the right. Add 'w' to each side of the equation. 4g + -1w + w = 0 + w Combine like terms: -1w + w = 0 4g + 0 = 0 + w 4g = 0 + w Remove the zero: 4g = w Divide each side by '4'. g = 0.25w Simplifying g = 0.25wSolution
g = {-0.125w, 0.25w}
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