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Simplifying 0 = -16t2 + 4t + 56 Reorder the terms: 0 = 56 + 4t + -16t2 Solving 0 = 56 + 4t + -16t2 Solving for variable 't'. Combine like terms: 0 + -56 = -56 -56 + -4t + 16t2 = 56 + 4t + -16t2 + -56 + -4t + 16t2 Reorder the terms: -56 + -4t + 16t2 = 56 + -56 + 4t + -4t + -16t2 + 16t2 Combine like terms: 56 + -56 = 0 -56 + -4t + 16t2 = 0 + 4t + -4t + -16t2 + 16t2 -56 + -4t + 16t2 = 4t + -4t + -16t2 + 16t2 Combine like terms: 4t + -4t = 0 -56 + -4t + 16t2 = 0 + -16t2 + 16t2 -56 + -4t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -56 + -4t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-14 + -1t + 4t2) = 0 Factor a trinomial. 4((-7 + -4t)(2 + -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 '(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 = {-1.75, 2}
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