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Simplifying 420 = -16t2 + 52t + 560 Reorder the terms: 420 = 560 + 52t + -16t2 Solving 420 = 560 + 52t + -16t2 Solving for variable 't'. Combine like terms: 420 + -560 = -140 -140 + -52t + 16t2 = 560 + 52t + -16t2 + -560 + -52t + 16t2 Reorder the terms: -140 + -52t + 16t2 = 560 + -560 + 52t + -52t + -16t2 + 16t2 Combine like terms: 560 + -560 = 0 -140 + -52t + 16t2 = 0 + 52t + -52t + -16t2 + 16t2 -140 + -52t + 16t2 = 52t + -52t + -16t2 + 16t2 Combine like terms: 52t + -52t = 0 -140 + -52t + 16t2 = 0 + -16t2 + 16t2 -140 + -52t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -140 + -52t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-35 + -13t + 4t2) = 0 Factor a trinomial. 4((-7 + -4t)(5 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + -4t)' equal to zero and attempt to solve: Simplifying -7 + -4t = 0 Solving -7 + -4t = 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 + -4t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4t = 0 + 7 -4t = 0 + 7 Combine like terms: 0 + 7 = 7 -4t = 7 Divide each side by '-4'. t = -1.75 Simplifying t = -1.75Subproblem 2
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 = 5Solution
t = {-1.75, 5}
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