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Simplifying 18a2 + -39at + 20t2 = 0 Reorder the terms: -39at + 18a2 + 20t2 = 0 Solving -39at + 18a2 + 20t2 = 0 Solving for variable 'a'. Factor a trinomial. (3a + -4t)(6a + -5t) = 0Subproblem 1
Set the factor '(3a + -4t)' equal to zero and attempt to solve: Simplifying 3a + -4t = 0 Solving 3a + -4t = 0 Move all terms containing a to the left, all other terms to the right. Add '4t' to each side of the equation. 3a + -4t + 4t = 0 + 4t Combine like terms: -4t + 4t = 0 3a + 0 = 0 + 4t 3a = 0 + 4t Remove the zero: 3a = 4t Divide each side by '3'. a = 1.333333333t Simplifying a = 1.333333333tSubproblem 2
Set the factor '(6a + -5t)' equal to zero and attempt to solve: Simplifying 6a + -5t = 0 Solving 6a + -5t = 0 Move all terms containing a to the left, all other terms to the right. Add '5t' to each side of the equation. 6a + -5t + 5t = 0 + 5t Combine like terms: -5t + 5t = 0 6a + 0 = 0 + 5t 6a = 0 + 5t Remove the zero: 6a = 5t Divide each side by '6'. a = 0.8333333333t Simplifying a = 0.8333333333tSolution
a = {1.333333333t, 0.8333333333t}
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