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Simplifying t2 + 5tg + -24g2 = 0 Reorder the terms: 5gt + -24g2 + t2 = 0 Solving 5gt + -24g2 + t2 = 0 Solving for variable 'g'. Factor a trinomial. (-8g + -1t)(3g + -1t) = 0Subproblem 1
Set the factor '(-8g + -1t)' equal to zero and attempt to solve: Simplifying -8g + -1t = 0 Solving -8g + -1t = 0 Move all terms containing g to the left, all other terms to the right. Add 't' to each side of the equation. -8g + -1t + t = 0 + t Combine like terms: -1t + t = 0 -8g + 0 = 0 + t -8g = 0 + t Remove the zero: -8g = t Divide each side by '-8'. g = -0.125t Simplifying g = -0.125tSubproblem 2
Set the factor '(3g + -1t)' equal to zero and attempt to solve: Simplifying 3g + -1t = 0 Solving 3g + -1t = 0 Move all terms containing g to the left, all other terms to the right. Add 't' to each side of the equation. 3g + -1t + t = 0 + t Combine like terms: -1t + t = 0 3g + 0 = 0 + t 3g = 0 + t Remove the zero: 3g = t Divide each side by '3'. g = 0.3333333333t Simplifying g = 0.3333333333tSolution
g = {-0.125t, 0.3333333333t}
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