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Simplifying 4t + -9t + 16 = 15 + -4t2 Reorder the terms: 16 + 4t + -9t = 15 + -4t2 Combine like terms: 4t + -9t = -5t 16 + -5t = 15 + -4t2 Solving 16 + -5t = 15 + -4t2 Solving for variable 't'. Reorder the terms: 16 + -15 + -5t + 4t2 = 15 + -4t2 + -15 + 4t2 Combine like terms: 16 + -15 = 1 1 + -5t + 4t2 = 15 + -4t2 + -15 + 4t2 Reorder the terms: 1 + -5t + 4t2 = 15 + -15 + -4t2 + 4t2 Combine like terms: 15 + -15 = 0 1 + -5t + 4t2 = 0 + -4t2 + 4t2 1 + -5t + 4t2 = -4t2 + 4t2 Combine like terms: -4t2 + 4t2 = 0 1 + -5t + 4t2 = 0 Factor a trinomial. (1 + -4t)(1 + -1t) = 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 '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 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 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {0.25, 1}
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