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Simplifying 42a2 + 17at + -15t2 = 0 Reorder the terms: 17at + 42a2 + -15t2 = 0 Solving 17at + 42a2 + -15t2 = 0 Solving for variable 'a'. Factor a trinomial. (7a + -3t)(6a + 5t) = 0Subproblem 1
Set the factor '(7a + -3t)' equal to zero and attempt to solve: Simplifying 7a + -3t = 0 Solving 7a + -3t = 0 Move all terms containing a to the left, all other terms to the right. Add '3t' to each side of the equation. 7a + -3t + 3t = 0 + 3t Combine like terms: -3t + 3t = 0 7a + 0 = 0 + 3t 7a = 0 + 3t Remove the zero: 7a = 3t Divide each side by '7'. a = 0.4285714286t Simplifying a = 0.4285714286tSubproblem 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 = {0.4285714286t, -0.8333333333t}
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