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Simplifying 16t2 = 32t + 9 Reorder the terms: 16t2 = 9 + 32t Solving 16t2 = 9 + 32t Solving for variable 't'. Reorder the terms: -9 + -32t + 16t2 = 9 + 32t + -9 + -32t Reorder the terms: -9 + -32t + 16t2 = 9 + -9 + 32t + -32t Combine like terms: 9 + -9 = 0 -9 + -32t + 16t2 = 0 + 32t + -32t -9 + -32t + 16t2 = 32t + -32t Combine like terms: 32t + -32t = 0 -9 + -32t + 16t2 = 0 Factor a trinomial. (-1 + -4t)(9 + -4t) = 0Subproblem 1
Set the factor '(-1 + -4t)' equal to zero and attempt to solve: Simplifying -1 + -4t = 0 Solving -1 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -4t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4t = 0 + 1 -4t = 0 + 1 Combine like terms: 0 + 1 = 1 -4t = 1 Divide each side by '-4'. t = -0.25 Simplifying t = -0.25Subproblem 2
Set the factor '(9 + -4t)' equal to zero and attempt to solve: Simplifying 9 + -4t = 0 Solving 9 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4t = 0 + -9 -4t = 0 + -9 Combine like terms: 0 + -9 = -9 -4t = -9 Divide each side by '-4'. t = 2.25 Simplifying t = 2.25Solution
t = {-0.25, 2.25}
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