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Simplifying 70 = -16t2 + 6t + 80 Reorder the terms: 70 = 80 + 6t + -16t2 Solving 70 = 80 + 6t + -16t2 Solving for variable 't'. Combine like terms: 70 + -80 = -10 -10 + -6t + 16t2 = 80 + 6t + -16t2 + -80 + -6t + 16t2 Reorder the terms: -10 + -6t + 16t2 = 80 + -80 + 6t + -6t + -16t2 + 16t2 Combine like terms: 80 + -80 = 0 -10 + -6t + 16t2 = 0 + 6t + -6t + -16t2 + 16t2 -10 + -6t + 16t2 = 6t + -6t + -16t2 + 16t2 Combine like terms: 6t + -6t = 0 -10 + -6t + 16t2 = 0 + -16t2 + 16t2 -10 + -6t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -10 + -6t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -3t + 8t2) = 0 Factor a trinomial. 2((-5 + -8t)(1 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -8t)' equal to zero and attempt to solve: Simplifying -5 + -8t = 0 Solving -5 + -8t = 0 Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -8t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8t = 0 + 5 -8t = 0 + 5 Combine like terms: 0 + 5 = 5 -8t = 5 Divide each side by '-8'. t = -0.625 Simplifying t = -0.625Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 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 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {-0.625, 1}
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