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Simplifying 30 = -16t2 + 45t + 4 Reorder the terms: 30 = 4 + 45t + -16t2 Solving 30 = 4 + 45t + -16t2 Solving for variable 't'. Combine like terms: 30 + -4 = 26 26 + -45t + 16t2 = 4 + 45t + -16t2 + -4 + -45t + 16t2 Reorder the terms: 26 + -45t + 16t2 = 4 + -4 + 45t + -45t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 26 + -45t + 16t2 = 0 + 45t + -45t + -16t2 + 16t2 26 + -45t + 16t2 = 45t + -45t + -16t2 + 16t2 Combine like terms: 45t + -45t = 0 26 + -45t + 16t2 = 0 + -16t2 + 16t2 26 + -45t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 26 + -45t + 16t2 = 0 Factor a trinomial. (13 + -16t)(2 + -1t) = 0Subproblem 1
Set the factor '(13 + -16t)' equal to zero and attempt to solve: Simplifying 13 + -16t = 0 Solving 13 + -16t = 0 Move all terms containing t to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -16t = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -16t = 0 + -13 -16t = 0 + -13 Combine like terms: 0 + -13 = -13 -16t = -13 Divide each side by '-16'. t = 0.8125 Simplifying t = 0.8125Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Solution
t = {0.8125, 2}
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