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Simplifying 2a2 + 3at + -9t2 = 0 Reorder the terms: 3at + 2a2 + -9t2 = 0 Solving 3at + 2a2 + -9t2 = 0 Solving for variable 'a'. Factor a trinomial. (2a + -3t)(a + 3t) = 0Subproblem 1
Set the factor '(2a + -3t)' equal to zero and attempt to solve: Simplifying 2a + -3t = 0 Solving 2a + -3t = 0 Move all terms containing a to the left, all other terms to the right. Add '3t' to each side of the equation. 2a + -3t + 3t = 0 + 3t Combine like terms: -3t + 3t = 0 2a + 0 = 0 + 3t 2a = 0 + 3t Remove the zero: 2a = 3t Divide each side by '2'. a = 1.5t Simplifying a = 1.5tSubproblem 2
Set the factor '(a + 3t)' equal to zero and attempt to solve: Simplifying a + 3t = 0 Solving a + 3t = 0 Move all terms containing a to the left, all other terms to the right. Add '-3t' to each side of the equation. a + 3t + -3t = 0 + -3t Combine like terms: 3t + -3t = 0 a + 0 = 0 + -3t a = 0 + -3t Remove the zero: a = -3t Simplifying a = -3tSolution
a = {1.5t, -3t}
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