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Simplifying s2 + 6sg + -16g2 = 0 Reorder the terms: 6gs + -16g2 + s2 = 0 Solving 6gs + -16g2 + s2 = 0 Solving for variable 'g'. Factor a trinomial. (-8g + -1s)(2g + -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 '(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 = 0.5sSolution
g = {-0.125s, 0.5s}
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