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Simplifying 0 = -16t2 + 160t + 176 Reorder the terms: 0 = 176 + 160t + -16t2 Solving 0 = 176 + 160t + -16t2 Solving for variable 't'. Combine like terms: 0 + -176 = -176 -176 + -160t + 16t2 = 176 + 160t + -16t2 + -176 + -160t + 16t2 Reorder the terms: -176 + -160t + 16t2 = 176 + -176 + 160t + -160t + -16t2 + 16t2 Combine like terms: 176 + -176 = 0 -176 + -160t + 16t2 = 0 + 160t + -160t + -16t2 + 16t2 -176 + -160t + 16t2 = 160t + -160t + -16t2 + 16t2 Combine like terms: 160t + -160t = 0 -176 + -160t + 16t2 = 0 + -16t2 + 16t2 -176 + -160t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -176 + -160t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-11 + -10t + t2) = 0 Factor a trinomial. 16((-1 + -1t)(11 + -1t)) = 0 Ignore the factor 16.Subproblem 1
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 = -1Subproblem 2
Set the factor '(11 + -1t)' equal to zero and attempt to solve: Simplifying 11 + -1t = 0 Solving 11 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1t = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1t = 0 + -11 -1t = 0 + -11 Combine like terms: 0 + -11 = -11 -1t = -11 Divide each side by '-1'. t = 11 Simplifying t = 11Solution
t = {-1, 11}
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