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Simplifying -16t2 + 92t = 76 Reorder the terms: 92t + -16t2 = 76 Solving 92t + -16t2 = 76 Solving for variable 't'. Reorder the terms: -76 + 92t + -16t2 = 76 + -76 Combine like terms: 76 + -76 = 0 -76 + 92t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-19 + 23t + -4t2) = 0 Factor a trinomial. 4((-19 + 4t)(1 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-19 + 4t)' equal to zero and attempt to solve: Simplifying -19 + 4t = 0 Solving -19 + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + 4t = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 4t = 0 + 19 4t = 0 + 19 Combine like terms: 0 + 19 = 19 4t = 19 Divide each side by '4'. t = 4.75 Simplifying t = 4.75Subproblem 2
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 = 1Solution
t = {4.75, 1}
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