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Simplifying 190 = -16t2 + 12t + 200 Reorder the terms: 190 = 200 + 12t + -16t2 Solving 190 = 200 + 12t + -16t2 Solving for variable 't'. Combine like terms: 190 + -200 = -10 -10 + -12t + 16t2 = 200 + 12t + -16t2 + -200 + -12t + 16t2 Reorder the terms: -10 + -12t + 16t2 = 200 + -200 + 12t + -12t + -16t2 + 16t2 Combine like terms: 200 + -200 = 0 -10 + -12t + 16t2 = 0 + 12t + -12t + -16t2 + 16t2 -10 + -12t + 16t2 = 12t + -12t + -16t2 + 16t2 Combine like terms: 12t + -12t = 0 -10 + -12t + 16t2 = 0 + -16t2 + 16t2 -10 + -12t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -10 + -12t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -6t + 8t2) = 0 Factor a trinomial. 2((-1 + -2t)(5 + -4t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -2t)' equal to zero and attempt to solve: Simplifying -1 + -2t = 0 Solving -1 + -2t = 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 + -2t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2t = 0 + 1 -2t = 0 + 1 Combine like terms: 0 + 1 = 1 -2t = 1 Divide each side by '-2'. t = -0.5 Simplifying t = -0.5Subproblem 2
Set the factor '(5 + -4t)' equal to zero and attempt to solve: Simplifying 5 + -4t = 0 Solving 5 + -4t = 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 + -4t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4t = 0 + -5 -4t = 0 + -5 Combine like terms: 0 + -5 = -5 -4t = -5 Divide each side by '-4'. t = 1.25 Simplifying t = 1.25Solution
t = {-0.5, 1.25}
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