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Simplifying 288 = -16t2 + 176t Reorder the terms: 288 = 176t + -16t2 Solving 288 = 176t + -16t2 Solving for variable 't'. Reorder the terms: 288 + -176t + 16t2 = 176t + -176t + -16t2 + 16t2 Combine like terms: 176t + -176t = 0 288 + -176t + 16t2 = 0 + -16t2 + 16t2 288 + -176t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 288 + -176t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(18 + -11t + t2) = 0 Factor a trinomial. 16((2 + -1t)(9 + -1t)) = 0 Ignore the factor 16.Subproblem 1
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 = 2Subproblem 2
Set the factor '(9 + -1t)' equal to zero and attempt to solve: Simplifying 9 + -1t = 0 Solving 9 + -1t = 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 + -1t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1t = 0 + -9 -1t = 0 + -9 Combine like terms: 0 + -9 = -9 -1t = -9 Divide each side by '-1'. t = 9 Simplifying t = 9Solution
t = {2, 9}
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