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Simplifying 0 = -32 + 16t2 + -16t Reorder the terms: 0 = -32 + -16t + 16t2 Solving 0 = -32 + -16t + 16t2 Solving for variable 't'. Combine like terms: 0 + 32 = 32 32 + 16t + -16t2 = -32 + -16t + 16t2 + 32 + 16t + -16t2 Reorder the terms: 32 + 16t + -16t2 = -32 + 32 + -16t + 16t + 16t2 + -16t2 Combine like terms: -32 + 32 = 0 32 + 16t + -16t2 = 0 + -16t + 16t + 16t2 + -16t2 32 + 16t + -16t2 = -16t + 16t + 16t2 + -16t2 Combine like terms: -16t + 16t = 0 32 + 16t + -16t2 = 0 + 16t2 + -16t2 32 + 16t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 32 + 16t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(2 + t + -1t2) = 0 Factor a trinomial. 16((2 + -1t)(1 + t)) = 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 '(1 + t)' equal to zero and attempt to solve: Simplifying 1 + t = 0 Solving 1 + t = 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 + t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + t = 0 + -1 t = 0 + -1 Combine like terms: 0 + -1 = -1 t = -1 Simplifying t = -1Solution
t = {2, -1}
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