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Simplifying 18q2 + -39qt + -189t2 = 0 Reorder the terms: -39qt + 18q2 + -189t2 = 0 Solving -39qt + 18q2 + -189t2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '3'. 3(-13qt + 6q2 + -63t2) = 0 Factor a trinomial. 3((2q + -9t)(3q + 7t)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2q + -9t)' equal to zero and attempt to solve: Simplifying 2q + -9t = 0 Solving 2q + -9t = 0 Move all terms containing q to the left, all other terms to the right. Add '9t' to each side of the equation. 2q + -9t + 9t = 0 + 9t Combine like terms: -9t + 9t = 0 2q + 0 = 0 + 9t 2q = 0 + 9t Remove the zero: 2q = 9t Divide each side by '2'. q = 4.5t Simplifying q = 4.5tSubproblem 2
Set the factor '(3q + 7t)' equal to zero and attempt to solve: Simplifying 3q + 7t = 0 Solving 3q + 7t = 0 Move all terms containing q to the left, all other terms to the right. Add '-7t' to each side of the equation. 3q + 7t + -7t = 0 + -7t Combine like terms: 7t + -7t = 0 3q + 0 = 0 + -7t 3q = 0 + -7t Remove the zero: 3q = -7t Divide each side by '3'. q = -2.333333333t Simplifying q = -2.333333333tSolution
q = {4.5t, -2.333333333t}
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