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Simplifying 20a2 + -27at + 9t2 = 0 Reorder the terms: -27at + 20a2 + 9t2 = 0 Solving -27at + 20a2 + 9t2 = 0 Solving for variable 'a'. Factor a trinomial. (4a + -3t)(5a + -3t) = 0Subproblem 1
Set the factor '(4a + -3t)' equal to zero and attempt to solve: Simplifying 4a + -3t = 0 Solving 4a + -3t = 0 Move all terms containing a to the left, all other terms to the right. Add '3t' to each side of the equation. 4a + -3t + 3t = 0 + 3t Combine like terms: -3t + 3t = 0 4a + 0 = 0 + 3t 4a = 0 + 3t Remove the zero: 4a = 3t Divide each side by '4'. a = 0.75t Simplifying a = 0.75tSubproblem 2
Set the factor '(5a + -3t)' equal to zero and attempt to solve: Simplifying 5a + -3t = 0 Solving 5a + -3t = 0 Move all terms containing a to the left, all other terms to the right. Add '3t' to each side of the equation. 5a + -3t + 3t = 0 + 3t Combine like terms: -3t + 3t = 0 5a + 0 = 0 + 3t 5a = 0 + 3t Remove the zero: 5a = 3t Divide each side by '5'. a = 0.6t Simplifying a = 0.6tSolution
a = {0.75t, 0.6t}
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