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Simplifying -16t2 + 20t + 300 = 0 Reorder the terms: 300 + 20t + -16t2 = 0 Solving 300 + 20t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(75 + 5t + -4t2) = 0 Factor a trinomial. 4((5 + -1t)(15 + 4t)) = 0 Ignore the factor 4.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 '(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 = {5, -3.75}
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