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Simplifying 370 = -16t2 + -4t + 382 Reorder the terms: 370 = 382 + -4t + -16t2 Solving 370 = 382 + -4t + -16t2 Solving for variable 't'. Combine like terms: 370 + -382 = -12 -12 + 4t + 16t2 = 382 + -4t + -16t2 + -382 + 4t + 16t2 Reorder the terms: -12 + 4t + 16t2 = 382 + -382 + -4t + 4t + -16t2 + 16t2 Combine like terms: 382 + -382 = 0 -12 + 4t + 16t2 = 0 + -4t + 4t + -16t2 + 16t2 -12 + 4t + 16t2 = -4t + 4t + -16t2 + 16t2 Combine like terms: -4t + 4t = 0 -12 + 4t + 16t2 = 0 + -16t2 + 16t2 -12 + 4t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -12 + 4t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + t + 4t2) = 0 Factor a trinomial. 4((-1 + -1t)(3 + -4t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -1t)' equal to zero and attempt to solve: Simplifying -1 + -1t = 0 Solving -1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1t = 0 + 1 -1t = 0 + 1 Combine like terms: 0 + 1 = 1 -1t = 1 Divide each side by '-1'. t = -1 Simplifying t = -1Subproblem 2
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 = 0.75Solution
t = {-1, 0.75}
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