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Simplifying 100 = -16t2 + 32t + 228 Reorder the terms: 100 = 228 + 32t + -16t2 Solving 100 = 228 + 32t + -16t2 Solving for variable 't'. Combine like terms: 100 + -228 = -128 -128 + -32t + 16t2 = 228 + 32t + -16t2 + -228 + -32t + 16t2 Reorder the terms: -128 + -32t + 16t2 = 228 + -228 + 32t + -32t + -16t2 + 16t2 Combine like terms: 228 + -228 = 0 -128 + -32t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2 -128 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2 Combine like terms: 32t + -32t = 0 -128 + -32t + 16t2 = 0 + -16t2 + 16t2 -128 + -32t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -128 + -32t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-8 + -2t + t2) = 0 Factor a trinomial. 16((-2 + -1t)(4 + -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 '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {-2, 4}
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