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Simplifying 252 = -16t2 + 20t + 336 Reorder the terms: 252 = 336 + 20t + -16t2 Solving 252 = 336 + 20t + -16t2 Solving for variable 't'. Combine like terms: 252 + -336 = -84 -84 + -20t + 16t2 = 336 + 20t + -16t2 + -336 + -20t + 16t2 Reorder the terms: -84 + -20t + 16t2 = 336 + -336 + 20t + -20t + -16t2 + 16t2 Combine like terms: 336 + -336 = 0 -84 + -20t + 16t2 = 0 + 20t + -20t + -16t2 + 16t2 -84 + -20t + 16t2 = 20t + -20t + -16t2 + 16t2 Combine like terms: 20t + -20t = 0 -84 + -20t + 16t2 = 0 + -16t2 + 16t2 -84 + -20t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -84 + -20t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-21 + -5t + 4t2) = 0 Factor a trinomial. 4((-7 + -4t)(3 + -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 '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 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 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {-1.75, 3}
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