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Simplifying 0 = -16t2 + 32t + 560 Reorder the terms: 0 = 560 + 32t + -16t2 Solving 0 = 560 + 32t + -16t2 Solving for variable 't'. Combine like terms: 0 + -560 = -560 -560 + -32t + 16t2 = 560 + 32t + -16t2 + -560 + -32t + 16t2 Reorder the terms: -560 + -32t + 16t2 = 560 + -560 + 32t + -32t + -16t2 + 16t2 Combine like terms: 560 + -560 = 0 -560 + -32t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2 -560 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2 Combine like terms: 32t + -32t = 0 -560 + -32t + 16t2 = 0 + -16t2 + 16t2 -560 + -32t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -560 + -32t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-35 + -2t + t2) = 0 Factor a trinomial. 16((-5 + -1t)(7 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-5 + -1t)' equal to zero and attempt to solve: Simplifying -5 + -1t = 0 Solving -5 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1t = 0 + 5 -1t = 0 + 5 Combine like terms: 0 + 5 = 5 -1t = 5 Divide each side by '-1'. t = -5 Simplifying t = -5Subproblem 2
Set the factor '(7 + -1t)' equal to zero and attempt to solve: Simplifying 7 + -1t = 0 Solving 7 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1t = 0 + -7 -1t = 0 + -7 Combine like terms: 0 + -7 = -7 -1t = -7 Divide each side by '-1'. t = 7 Simplifying t = 7Solution
t = {-5, 7}
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