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Simplifying 20a2 + -41at + 20t2 = 0 Reorder the terms: -41at + 20a2 + 20t2 = 0 Solving -41at + 20a2 + 20t2 = 0 Solving for variable 'a'. Factor a trinomial. (4a + -5t)(5a + -4t) = 0Subproblem 1
Set the factor '(4a + -5t)' equal to zero and attempt to solve: Simplifying 4a + -5t = 0 Solving 4a + -5t = 0 Move all terms containing a to the left, all other terms to the right. Add '5t' to each side of the equation. 4a + -5t + 5t = 0 + 5t Combine like terms: -5t + 5t = 0 4a + 0 = 0 + 5t 4a = 0 + 5t Remove the zero: 4a = 5t Divide each side by '4'. a = 1.25t Simplifying a = 1.25tSubproblem 2
Set the factor '(5a + -4t)' equal to zero and attempt to solve: Simplifying 5a + -4t = 0 Solving 5a + -4t = 0 Move all terms containing a to the left, all other terms to the right. Add '4t' to each side of the equation. 5a + -4t + 4t = 0 + 4t Combine like terms: -4t + 4t = 0 5a + 0 = 0 + 4t 5a = 0 + 4t Remove the zero: 5a = 4t Divide each side by '5'. a = 0.8t Simplifying a = 0.8tSolution
a = {1.25t, 0.8t}
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