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Simplifying t = -16t2 + -17t + 100 Reorder the terms: t = 100 + -17t + -16t2 Solving t = 100 + -17t + -16t2 Solving for variable 't'. Reorder the terms: -100 + t + 17t + 16t2 = 100 + -17t + -16t2 + -100 + 17t + 16t2 Combine like terms: t + 17t = 18t -100 + 18t + 16t2 = 100 + -17t + -16t2 + -100 + 17t + 16t2 Reorder the terms: -100 + 18t + 16t2 = 100 + -100 + -17t + 17t + -16t2 + 16t2 Combine like terms: 100 + -100 = 0 -100 + 18t + 16t2 = 0 + -17t + 17t + -16t2 + 16t2 -100 + 18t + 16t2 = -17t + 17t + -16t2 + 16t2 Combine like terms: -17t + 17t = 0 -100 + 18t + 16t2 = 0 + -16t2 + 16t2 -100 + 18t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -100 + 18t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + 9t + 8t2) = 0 Factor a trinomial. 2((-25 + -8t)(2 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + -8t)' equal to zero and attempt to solve: Simplifying -25 + -8t = 0 Solving -25 + -8t = 0 Move all terms containing t to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + -8t = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -8t = 0 + 25 -8t = 0 + 25 Combine like terms: 0 + 25 = 25 -8t = 25 Divide each side by '-8'. t = -3.125 Simplifying t = -3.125Subproblem 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 = {-3.125, 2}
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