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Simplifying 252 = -16t2 + 90t + 288 Reorder the terms: 252 = 288 + 90t + -16t2 Solving 252 = 288 + 90t + -16t2 Solving for variable 't'. Combine like terms: 252 + -288 = -36 -36 + -90t + 16t2 = 288 + 90t + -16t2 + -288 + -90t + 16t2 Reorder the terms: -36 + -90t + 16t2 = 288 + -288 + 90t + -90t + -16t2 + 16t2 Combine like terms: 288 + -288 = 0 -36 + -90t + 16t2 = 0 + 90t + -90t + -16t2 + 16t2 -36 + -90t + 16t2 = 90t + -90t + -16t2 + 16t2 Combine like terms: 90t + -90t = 0 -36 + -90t + 16t2 = 0 + -16t2 + 16t2 -36 + -90t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -36 + -90t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + -45t + 8t2) = 0 Factor a trinomial. 2((-3 + -8t)(6 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -8t)' equal to zero and attempt to solve: Simplifying -3 + -8t = 0 Solving -3 + -8t = 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 + -8t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8t = 0 + 3 -8t = 0 + 3 Combine like terms: 0 + 3 = 3 -8t = 3 Divide each side by '-8'. t = -0.375 Simplifying t = -0.375Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve: Simplifying 6 + -1t = 0 Solving 6 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1t = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1t = 0 + -6 -1t = 0 + -6 Combine like terms: 0 + -6 = -6 -1t = -6 Divide each side by '-1'. t = 6 Simplifying t = 6Solution
t = {-0.375, 6}
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