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Simplifying r2 + 6rg + -16g2 = 0 Reorder the terms: 6gr + -16g2 + r2 = 0 Solving 6gr + -16g2 + r2 = 0 Solving for variable 'g'. Factor a trinomial. (-8g + -1r)(2g + -1r) = 0Subproblem 1
Set the factor '(-8g + -1r)' equal to zero and attempt to solve: Simplifying -8g + -1r = 0 Solving -8g + -1r = 0 Move all terms containing g to the left, all other terms to the right. Add 'r' to each side of the equation. -8g + -1r + r = 0 + r Combine like terms: -1r + r = 0 -8g + 0 = 0 + r -8g = 0 + r Remove the zero: -8g = r Divide each side by '-8'. g = -0.125r Simplifying g = -0.125rSubproblem 2
Set the factor '(2g + -1r)' equal to zero and attempt to solve: Simplifying 2g + -1r = 0 Solving 2g + -1r = 0 Move all terms containing g to the left, all other terms to the right. Add 'r' to each side of the equation. 2g + -1r + r = 0 + r Combine like terms: -1r + r = 0 2g + 0 = 0 + r 2g = 0 + r Remove the zero: 2g = r Divide each side by '2'. g = 0.5r Simplifying g = 0.5rSolution
g = {-0.125r, 0.5r}
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