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Simplifying 648 = -16t2 + 60t + 864 Reorder the terms: 648 = 864 + 60t + -16t2 Solving 648 = 864 + 60t + -16t2 Solving for variable 't'. Combine like terms: 648 + -864 = -216 -216 + -60t + 16t2 = 864 + 60t + -16t2 + -864 + -60t + 16t2 Reorder the terms: -216 + -60t + 16t2 = 864 + -864 + 60t + -60t + -16t2 + 16t2 Combine like terms: 864 + -864 = 0 -216 + -60t + 16t2 = 0 + 60t + -60t + -16t2 + 16t2 -216 + -60t + 16t2 = 60t + -60t + -16t2 + 16t2 Combine like terms: 60t + -60t = 0 -216 + -60t + 16t2 = 0 + -16t2 + 16t2 -216 + -60t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -216 + -60t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-54 + -15t + 4t2) = 0 Factor a trinomial. 4((-9 + -4t)(6 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + -4t)' equal to zero and attempt to solve: Simplifying -9 + -4t = 0 Solving -9 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -4t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4t = 0 + 9 -4t = 0 + 9 Combine like terms: 0 + 9 = 9 -4t = 9 Divide each side by '-4'. t = -2.25 Simplifying t = -2.25Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve: Simplifying 6 + -1t = 0 Solving 6 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1t = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1t = 0 + -6 -1t = 0 + -6 Combine like terms: 0 + -6 = -6 -1t = -6 Divide each side by '-1'. t = 6 Simplifying t = 6Solution
t = {-2.25, 6}
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