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Simplifying 0 = -16t2 + 14t + 36 Reorder the terms: 0 = 36 + 14t + -16t2 Solving 0 = 36 + 14t + -16t2 Solving for variable 't'. Combine like terms: 0 + -36 = -36 -36 + -14t + 16t2 = 36 + 14t + -16t2 + -36 + -14t + 16t2 Reorder the terms: -36 + -14t + 16t2 = 36 + -36 + 14t + -14t + -16t2 + 16t2 Combine like terms: 36 + -36 = 0 -36 + -14t + 16t2 = 0 + 14t + -14t + -16t2 + 16t2 -36 + -14t + 16t2 = 14t + -14t + -16t2 + 16t2 Combine like terms: 14t + -14t = 0 -36 + -14t + 16t2 = 0 + -16t2 + 16t2 -36 + -14t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -36 + -14t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + -7t + 8t2) = 0 Factor a trinomial. 2((-9 + -8t)(2 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -8t)' equal to zero and attempt to solve: Simplifying -9 + -8t = 0 Solving -9 + -8t = 0 Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -8t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -8t = 0 + 9 -8t = 0 + 9 Combine like terms: 0 + 9 = 9 -8t = 9 Divide each side by '-8'. t = -1.125 Simplifying t = -1.125Subproblem 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 = {-1.125, 2}
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