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