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Simplifying 0 = -16t2 + 112t + 704 Reorder the terms: 0 = 704 + 112t + -16t2 Solving 0 = 704 + 112t + -16t2 Solving for variable 't'. Combine like terms: 0 + -704 = -704 -704 + -112t + 16t2 = 704 + 112t + -16t2 + -704 + -112t + 16t2 Reorder the terms: -704 + -112t + 16t2 = 704 + -704 + 112t + -112t + -16t2 + 16t2 Combine like terms: 704 + -704 = 0 -704 + -112t + 16t2 = 0 + 112t + -112t + -16t2 + 16t2 -704 + -112t + 16t2 = 112t + -112t + -16t2 + 16t2 Combine like terms: 112t + -112t = 0 -704 + -112t + 16t2 = 0 + -16t2 + 16t2 -704 + -112t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -704 + -112t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-44 + -7t + t2) = 0 Factor a trinomial. 16((-4 + -1t)(11 + -1t)) = 0 Ignore the factor 16.Subproblem 1
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 = -4Subproblem 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 = {-4, 11}
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