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Simplifying 12t2 = -62t + 22 Reorder the terms: 12t2 = 22 + -62t Solving 12t2 = 22 + -62t Solving for variable 't'. Reorder the terms: -22 + 62t + 12t2 = 22 + -62t + -22 + 62t Reorder the terms: -22 + 62t + 12t2 = 22 + -22 + -62t + 62t Combine like terms: 22 + -22 = 0 -22 + 62t + 12t2 = 0 + -62t + 62t -22 + 62t + 12t2 = -62t + 62t Combine like terms: -62t + 62t = 0 -22 + 62t + 12t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-11 + 31t + 6t2) = 0 Factor a trinomial. 2((-11 + -2t)(1 + -3t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + -2t)' equal to zero and attempt to solve: Simplifying -11 + -2t = 0 Solving -11 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -2t = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -2t = 0 + 11 -2t = 0 + 11 Combine like terms: 0 + 11 = 11 -2t = 11 Divide each side by '-2'. t = -5.5 Simplifying t = -5.5Subproblem 2
Set the factor '(1 + -3t)' equal to zero and attempt to solve: Simplifying 1 + -3t = 0 Solving 1 + -3t = 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 + -3t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3t = 0 + -1 -3t = 0 + -1 Combine like terms: 0 + -1 = -1 -3t = -1 Divide each side by '-3'. t = 0.3333333333 Simplifying t = 0.3333333333Solution
t = {-5.5, 0.3333333333}
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