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Simplifying w2 + 3wg + -40g2 = 0 Reorder the terms: 3gw + -40g2 + w2 = 0 Solving 3gw + -40g2 + w2 = 0 Solving for variable 'g'. Factor a trinomial. (-8g + -1w)(5g + -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 '(5g + -1w)' equal to zero and attempt to solve: Simplifying 5g + -1w = 0 Solving 5g + -1w = 0 Move all terms containing g to the left, all other terms to the right. Add 'w' to each side of the equation. 5g + -1w + w = 0 + w Combine like terms: -1w + w = 0 5g + 0 = 0 + w 5g = 0 + w Remove the zero: 5g = w Divide each side by '5'. g = 0.2w Simplifying g = 0.2wSolution
g = {-0.125w, 0.2w}
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