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Simplifying s2 + -3sg + -10g2 = 0 Reorder the terms: -3gs + -10g2 + s2 = 0 Solving -3gs + -10g2 + s2 = 0 Solving for variable 'g'. Factor a trinomial. (-2g + -1s)(5g + -1s) = 0Subproblem 1
Set the factor '(-2g + -1s)' equal to zero and attempt to solve: Simplifying -2g + -1s = 0 Solving -2g + -1s = 0 Move all terms containing g to the left, all other terms to the right. Add 's' to each side of the equation. -2g + -1s + s = 0 + s Combine like terms: -1s + s = 0 -2g + 0 = 0 + s -2g = 0 + s Remove the zero: -2g = s Divide each side by '-2'. g = -0.5s Simplifying g = -0.5sSubproblem 2
Set the factor '(5g + -1s)' equal to zero and attempt to solve: Simplifying 5g + -1s = 0 Solving 5g + -1s = 0 Move all terms containing g to the left, all other terms to the right. Add 's' to each side of the equation. 5g + -1s + s = 0 + s Combine like terms: -1s + s = 0 5g + 0 = 0 + s 5g = 0 + s Remove the zero: 5g = s Divide each side by '5'. g = 0.2s Simplifying g = 0.2sSolution
g = {-0.5s, 0.2s}
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