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Simplifying w2 + -11wg + 18g2 = 0 Reorder the terms: -11gw + 18g2 + w2 = 0 Solving -11gw + 18g2 + w2 = 0 Solving for variable 'g'. Factor a trinomial. (2g + -1w)(9g + -1w) = 0Subproblem 1
Set the factor '(2g + -1w)' equal to zero and attempt to solve: Simplifying 2g + -1w = 0 Solving 2g + -1w = 0 Move all terms containing g to the left, all other terms to the right. Add 'w' to each side of the equation. 2g + -1w + w = 0 + w Combine like terms: -1w + w = 0 2g + 0 = 0 + w 2g = 0 + w Remove the zero: 2g = w Divide each side by '2'. g = 0.5w Simplifying g = 0.5wSubproblem 2
Set the factor '(9g + -1w)' equal to zero and attempt to solve: Simplifying 9g + -1w = 0 Solving 9g + -1w = 0 Move all terms containing g to the left, all other terms to the right. Add 'w' to each side of the equation. 9g + -1w + w = 0 + w Combine like terms: -1w + w = 0 9g + 0 = 0 + w 9g = 0 + w Remove the zero: 9g = w Divide each side by '9'. g = 0.1111111111w Simplifying g = 0.1111111111wSolution
g = {0.5w, 0.1111111111w}
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