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Simplifying 2t + 13t2 + -3t2 + 17 + -16 + -10 + -11t = 0 Reorder the terms: 17 + -16 + -10 + 2t + -11t + 13t2 + -3t2 = 0 Combine like terms: 17 + -16 = 1 1 + -10 + 2t + -11t + 13t2 + -3t2 = 0 Combine like terms: 1 + -10 = -9 -9 + 2t + -11t + 13t2 + -3t2 = 0 Combine like terms: 2t + -11t = -9t -9 + -9t + 13t2 + -3t2 = 0 Combine like terms: 13t2 + -3t2 = 10t2 -9 + -9t + 10t2 = 0 Solving -9 + -9t + 10t2 = 0 Solving for variable 't'. Factor a trinomial. (-3 + -5t)(3 + -2t) = 0Subproblem 1
Set the factor '(-3 + -5t)' equal to zero and attempt to solve: Simplifying -3 + -5t = 0 Solving -3 + -5t = 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 + -5t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5t = 0 + 3 -5t = 0 + 3 Combine like terms: 0 + 3 = 3 -5t = 3 Divide each side by '-5'. t = -0.6 Simplifying t = -0.6Subproblem 2
Set the factor '(3 + -2t)' equal to zero and attempt to solve: Simplifying 3 + -2t = 0 Solving 3 + -2t = 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 + -2t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2t = 0 + -3 -2t = 0 + -3 Combine like terms: 0 + -3 = -3 -2t = -3 Divide each side by '-2'. t = 1.5 Simplifying t = 1.5Solution
t = {-0.6, 1.5}
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