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Simplifying 9a2 + -27at + 14t2 = 0 Reorder the terms: -27at + 9a2 + 14t2 = 0 Solving -27at + 9a2 + 14t2 = 0 Solving for variable 'a'. Factor a trinomial. (3a + -7t)(3a + -2t) = 0Subproblem 1
Set the factor '(3a + -7t)' equal to zero and attempt to solve: Simplifying 3a + -7t = 0 Solving 3a + -7t = 0 Move all terms containing a to the left, all other terms to the right. Add '7t' to each side of the equation. 3a + -7t + 7t = 0 + 7t Combine like terms: -7t + 7t = 0 3a + 0 = 0 + 7t 3a = 0 + 7t Remove the zero: 3a = 7t Divide each side by '3'. a = 2.333333333t Simplifying a = 2.333333333tSubproblem 2
Set the factor '(3a + -2t)' equal to zero and attempt to solve: Simplifying 3a + -2t = 0 Solving 3a + -2t = 0 Move all terms containing a to the left, all other terms to the right. Add '2t' to each side of the equation. 3a + -2t + 2t = 0 + 2t Combine like terms: -2t + 2t = 0 3a + 0 = 0 + 2t 3a = 0 + 2t Remove the zero: 3a = 2t Divide each side by '3'. a = 0.6666666667t Simplifying a = 0.6666666667tSolution
a = {2.333333333t, 0.6666666667t}
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