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Simplifying s2 + -4sg + -32g2 = 0 Reorder the terms: -4gs + -32g2 + s2 = 0 Solving -4gs + -32g2 + s2 = 0 Solving for variable 'g'. Factor a trinomial. (-4g + -1s)(8g + -1s) = 0Subproblem 1
Set the factor '(-4g + -1s)' equal to zero and attempt to solve: Simplifying -4g + -1s = 0 Solving -4g + -1s = 0 Move all terms containing g to the left, all other terms to the right. Add 's' to each side of the equation. -4g + -1s + s = 0 + s Combine like terms: -1s + s = 0 -4g + 0 = 0 + s -4g = 0 + s Remove the zero: -4g = s Divide each side by '-4'. g = -0.25s Simplifying g = -0.25sSubproblem 2
Set the factor '(8g + -1s)' equal to zero and attempt to solve: Simplifying 8g + -1s = 0 Solving 8g + -1s = 0 Move all terms containing g to the left, all other terms to the right. Add 's' to each side of the equation. 8g + -1s + s = 0 + s Combine like terms: -1s + s = 0 8g + 0 = 0 + s 8g = 0 + s Remove the zero: 8g = s Divide each side by '8'. g = 0.125s Simplifying g = 0.125sSolution
g = {-0.25s, 0.125s}
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