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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. (-8g + -1s)(4g + -1s) = 0Subproblem 1
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 = -0.125sSubproblem 2
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 = 0.25sSolution
g = {-0.125s, 0.25s}
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