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Simplifying 16t2 = 36 + 36t Solving 16t2 = 36 + 36t Solving for variable 't'. Reorder the terms: -36 + -36t + 16t2 = 36 + 36t + -36 + -36t Reorder the terms: -36 + -36t + 16t2 = 36 + -36 + 36t + -36t Combine like terms: 36 + -36 = 0 -36 + -36t + 16t2 = 0 + 36t + -36t -36 + -36t + 16t2 = 36t + -36t Combine like terms: 36t + -36t = 0 -36 + -36t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-9 + -9t + 4t2) = 0 Factor a trinomial. 4((-3 + -4t)(3 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -4t)' equal to zero and attempt to solve: Simplifying -3 + -4t = 0 Solving -3 + -4t = 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 + -4t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4t = 0 + 3 -4t = 0 + 3 Combine like terms: 0 + 3 = 3 -4t = 3 Divide each side by '-4'. t = -0.75 Simplifying t = -0.75Subproblem 2
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 = 3Solution
t = {-0.75, 3}
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