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Simplifying 276 = -16t2 + 20t + 300 Reorder the terms: 276 = 300 + 20t + -16t2 Solving 276 = 300 + 20t + -16t2 Solving for variable 't'. Combine like terms: 276 + -300 = -24 -24 + -20t + 16t2 = 300 + 20t + -16t2 + -300 + -20t + 16t2 Reorder the terms: -24 + -20t + 16t2 = 300 + -300 + 20t + -20t + -16t2 + 16t2 Combine like terms: 300 + -300 = 0 -24 + -20t + 16t2 = 0 + 20t + -20t + -16t2 + 16t2 -24 + -20t + 16t2 = 20t + -20t + -16t2 + 16t2 Combine like terms: 20t + -20t = 0 -24 + -20t + 16t2 = 0 + -16t2 + 16t2 -24 + -20t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -24 + -20t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + -5t + 4t2) = 0 Factor a trinomial. 4((-3 + -4t)(2 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -4t)' equal to zero and attempt to solve: Simplifying -3 + -4t = 0 Solving -3 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4t = 0 + 3 -4t = 0 + 3 Combine like terms: 0 + 3 = 3 -4t = 3 Divide each side by '-4'. t = -0.75 Simplifying t = -0.75Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Solution
t = {-0.75, 2}
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