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Simplifying 8 = 36t + -16t2 Solving 8 = 36t + -16t2 Solving for variable 't'. Reorder the terms: 8 + -36t + 16t2 = 36t + -36t + -16t2 + 16t2 Combine like terms: 36t + -36t = 0 8 + -36t + 16t2 = 0 + -16t2 + 16t2 8 + -36t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 8 + -36t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(2 + -9t + 4t2) = 0 Factor a trinomial. 4((1 + -4t)(2 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -4t)' equal to zero and attempt to solve: Simplifying 1 + -4t = 0 Solving 1 + -4t = 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 + -4t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4t = 0 + -1 -4t = 0 + -1 Combine like terms: 0 + -1 = -1 -4t = -1 Divide each side by '-4'. t = 0.25 Simplifying t = 0.25Subproblem 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 = {0.25, 2}
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