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Simplifying 18q2 + -39qt + 20t2 = 0 Reorder the terms: -39qt + 18q2 + 20t2 = 0 Solving -39qt + 18q2 + 20t2 = 0 Solving for variable 'q'. Factor a trinomial. (3q + -4t)(6q + -5t) = 0Subproblem 1
Set the factor '(3q + -4t)' equal to zero and attempt to solve: Simplifying 3q + -4t = 0 Solving 3q + -4t = 0 Move all terms containing q to the left, all other terms to the right. Add '4t' to each side of the equation. 3q + -4t + 4t = 0 + 4t Combine like terms: -4t + 4t = 0 3q + 0 = 0 + 4t 3q = 0 + 4t Remove the zero: 3q = 4t Divide each side by '3'. q = 1.333333333t Simplifying q = 1.333333333tSubproblem 2
Set the factor '(6q + -5t)' equal to zero and attempt to solve: Simplifying 6q + -5t = 0 Solving 6q + -5t = 0 Move all terms containing q to the left, all other terms to the right. Add '5t' to each side of the equation. 6q + -5t + 5t = 0 + 5t Combine like terms: -5t + 5t = 0 6q + 0 = 0 + 5t 6q = 0 + 5t Remove the zero: 6q = 5t Divide each side by '6'. q = 0.8333333333t Simplifying q = 0.8333333333tSolution
q = {1.333333333t, 0.8333333333t}
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