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Simplifying 9t2 + 2t + 25 = 32t Reorder the terms: 25 + 2t + 9t2 = 32t Solving 25 + 2t + 9t2 = 32t Solving for variable 't'. Reorder the terms: 25 + 2t + -32t + 9t2 = 32t + -32t Combine like terms: 2t + -32t = -30t 25 + -30t + 9t2 = 32t + -32t Combine like terms: 32t + -32t = 0 25 + -30t + 9t2 = 0 Factor a trinomial. (5 + -3t)(5 + -3t) = 0Subproblem 1
Set the factor '(5 + -3t)' equal to zero and attempt to solve: Simplifying 5 + -3t = 0 Solving 5 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3t = 0 + -5 -3t = 0 + -5 Combine like terms: 0 + -5 = -5 -3t = -5 Divide each side by '-3'. t = 1.666666667 Simplifying t = 1.666666667Subproblem 2
Set the factor '(5 + -3t)' equal to zero and attempt to solve: Simplifying 5 + -3t = 0 Solving 5 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3t = 0 + -5 -3t = 0 + -5 Combine like terms: 0 + -5 = -5 -3t = -5 Divide each side by '-3'. t = 1.666666667 Simplifying t = 1.666666667Solution
t = {1.666666667, 1.666666667}
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