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Simplifying 310 = -16t2 + -4t + 382 Reorder the terms: 310 = 382 + -4t + -16t2 Solving 310 = 382 + -4t + -16t2 Solving for variable 't'. Combine like terms: 310 + -382 = -72 -72 + 4t + 16t2 = 382 + -4t + -16t2 + -382 + 4t + 16t2 Reorder the terms: -72 + 4t + 16t2 = 382 + -382 + -4t + 4t + -16t2 + 16t2 Combine like terms: 382 + -382 = 0 -72 + 4t + 16t2 = 0 + -4t + 4t + -16t2 + 16t2 -72 + 4t + 16t2 = -4t + 4t + -16t2 + 16t2 Combine like terms: -4t + 4t = 0 -72 + 4t + 16t2 = 0 + -16t2 + 16t2 -72 + 4t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -72 + 4t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-18 + t + 4t2) = 0 Factor a trinomial. 4((-9 + -4t)(2 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + -4t)' equal to zero and attempt to solve: Simplifying -9 + -4t = 0 Solving -9 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -4t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4t = 0 + 9 -4t = 0 + 9 Combine like terms: 0 + 9 = 9 -4t = 9 Divide each side by '-4'. t = -2.25 Simplifying t = -2.25Subproblem 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 = {-2.25, 2}
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