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Simplifying 10 = -16t2 + 36t + -10 Reorder the terms: 10 = -10 + 36t + -16t2 Solving 10 = -10 + 36t + -16t2 Solving for variable 't'. Combine like terms: 10 + 10 = 20 20 + -36t + 16t2 = -10 + 36t + -16t2 + 10 + -36t + 16t2 Reorder the terms: 20 + -36t + 16t2 = -10 + 10 + 36t + -36t + -16t2 + 16t2 Combine like terms: -10 + 10 = 0 20 + -36t + 16t2 = 0 + 36t + -36t + -16t2 + 16t2 20 + -36t + 16t2 = 36t + -36t + -16t2 + 16t2 Combine like terms: 36t + -36t = 0 20 + -36t + 16t2 = 0 + -16t2 + 16t2 20 + -36t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 20 + -36t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(5 + -9t + 4t2) = 0 Factor a trinomial. 4((1 + -1t)(5 + -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 '(5 + -4t)' equal to zero and attempt to solve: Simplifying 5 + -4t = 0 Solving 5 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4t = 0 + -5 -4t = 0 + -5 Combine like terms: 0 + -5 = -5 -4t = -5 Divide each side by '-4'. t = 1.25 Simplifying t = 1.25Solution
t = {1, 1.25}
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