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Simplifying 0.1t(t + -8) = 1.1 + 0.3t Reorder the terms: 0.1t(-8 + t) = 1.1 + 0.3t (-8 * 0.1t + t * 0.1t) = 1.1 + 0.3t (-0.8t + 0.1t2) = 1.1 + 0.3t Solving -0.8t + 0.1t2 = 1.1 + 0.3t Solving for variable 't'. Reorder the terms: -1.1 + -0.8t + -0.3t + 0.1t2 = 1.1 + 0.3t + -1.1 + -0.3t Combine like terms: -0.8t + -0.3t = -1.1t -1.1 + -1.1t + 0.1t2 = 1.1 + 0.3t + -1.1 + -0.3t Reorder the terms: -1.1 + -1.1t + 0.1t2 = 1.1 + -1.1 + 0.3t + -0.3t Combine like terms: 1.1 + -1.1 = 0.0 -1.1 + -1.1t + 0.1t2 = 0.0 + 0.3t + -0.3t -1.1 + -1.1t + 0.1t2 = 0.3t + -0.3t Combine like terms: 0.3t + -0.3t = 0.0 -1.1 + -1.1t + 0.1t2 = 0.0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -11 + -11t + t2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -11t + 11 + t2 = 0 + 11 Reorder the terms: -11 + 11 + -11t + t2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -11t + t2 = 0 + 11 -11t + t2 = 0 + 11 Combine like terms: 0 + 11 = 11 -11t + t2 = 11 The t term is -11t. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11t + 30.25 + t2 = 11 + 30.25 Reorder the terms: 30.25 + -11t + t2 = 11 + 30.25 Combine like terms: 11 + 30.25 = 41.25 30.25 + -11t + t2 = 41.25 Factor a perfect square on the left side: (t + -5.5)(t + -5.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (t + -5.5) equal to 6.422616289 and -6.422616289.Subproblem 1
t + -5.5 = 6.422616289 Simplifying t + -5.5 = 6.422616289 Reorder the terms: -5.5 + t = 6.422616289 Solving -5.5 + t = 6.422616289 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + t = 6.422616289 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = 6.422616289 + 5.5 t = 6.422616289 + 5.5 Combine like terms: 6.422616289 + 5.5 = 11.922616289 t = 11.922616289 Simplifying t = 11.922616289Subproblem 2
t + -5.5 = -6.422616289 Simplifying t + -5.5 = -6.422616289 Reorder the terms: -5.5 + t = -6.422616289 Solving -5.5 + t = -6.422616289 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + t = -6.422616289 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = -6.422616289 + 5.5 t = -6.422616289 + 5.5 Combine like terms: -6.422616289 + 5.5 = -0.922616289 t = -0.922616289 Simplifying t = -0.922616289Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.922616289, -0.922616289}
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