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Simplifying 4t2 = 10 + 18t Solving 4t2 = 10 + 18t Solving for variable 't'. Reorder the terms: -10 + -18t + 4t2 = 10 + 18t + -10 + -18t Reorder the terms: -10 + -18t + 4t2 = 10 + -10 + 18t + -18t Combine like terms: 10 + -10 = 0 -10 + -18t + 4t2 = 0 + 18t + -18t -10 + -18t + 4t2 = 18t + -18t Combine like terms: 18t + -18t = 0 -10 + -18t + 4t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -9t + 2t2) = 0 Factor a trinomial. 2((-1 + -2t)(5 + -1t)) = 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 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 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 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5Solution
t = {-0.5, 5}
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