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Simplifying -16t2 + 68t + 480 = 0 Reorder the terms: 480 + 68t + -16t2 = 0 Solving 480 + 68t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(120 + 17t + -4t2) = 0 Factor a trinomial. 4((8 + -1t)(15 + 4t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(8 + -1t)' equal to zero and attempt to solve: Simplifying 8 + -1t = 0 Solving 8 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1t = 0 + -8 -1t = 0 + -8 Combine like terms: 0 + -8 = -8 -1t = -8 Divide each side by '-1'. t = 8 Simplifying t = 8Subproblem 2
Set the factor '(15 + 4t)' equal to zero and attempt to solve: Simplifying 15 + 4t = 0 Solving 15 + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + 4t = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 4t = 0 + -15 4t = 0 + -15 Combine like terms: 0 + -15 = -15 4t = -15 Divide each side by '4'. t = -3.75 Simplifying t = -3.75Solution
t = {8, -3.75}
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