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Simplifying w2 + 4wg + -45g2 = 0 Reorder the terms: 4gw + -45g2 + w2 = 0 Solving 4gw + -45g2 + w2 = 0 Solving for variable 'g'. Factor a trinomial. (-9g + -1w)(5g + -1w) = 0Subproblem 1
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 = -0.1111111111wSubproblem 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 = {-0.1111111111w, 0.2w}
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