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Simplifying 340 = -16t2 + -4t + 472 Reorder the terms: 340 = 472 + -4t + -16t2 Solving 340 = 472 + -4t + -16t2 Solving for variable 't'. Combine like terms: 340 + -472 = -132 -132 + 4t + 16t2 = 472 + -4t + -16t2 + -472 + 4t + 16t2 Reorder the terms: -132 + 4t + 16t2 = 472 + -472 + -4t + 4t + -16t2 + 16t2 Combine like terms: 472 + -472 = 0 -132 + 4t + 16t2 = 0 + -4t + 4t + -16t2 + 16t2 -132 + 4t + 16t2 = -4t + 4t + -16t2 + 16t2 Combine like terms: -4t + 4t = 0 -132 + 4t + 16t2 = 0 + -16t2 + 16t2 -132 + 4t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -132 + 4t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-33 + t + 4t2) = 0 Factor a trinomial. 4((-3 + -1t)(11 + -4t)) = 0 Ignore the factor 4.Subproblem 1
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 = -3Subproblem 2
Set the factor '(11 + -4t)' equal to zero and attempt to solve: Simplifying 11 + -4t = 0 Solving 11 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -4t = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -4t = 0 + -11 -4t = 0 + -11 Combine like terms: 0 + -11 = -11 -4t = -11 Divide each side by '-4'. t = 2.75 Simplifying t = 2.75Solution
t = {-3, 2.75}
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