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Simplifying 1.1t2 + -9.5t + -9.5 = 0 Reorder the terms: -9.5 + -9.5t + 1.1t2 = 0 Solving -9.5 + -9.5t + 1.1t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 1.1 the coefficient of the squared term: Divide each side by '1.1'. -8.636363636 + -8.636363636t + t2 = 0 Move the constant term to the right: Add '8.636363636' to each side of the equation. -8.636363636 + -8.636363636t + 8.636363636 + t2 = 0 + 8.636363636 Reorder the terms: -8.636363636 + 8.636363636 + -8.636363636t + t2 = 0 + 8.636363636 Combine like terms: -8.636363636 + 8.636363636 = 0.000000000 0.000000000 + -8.636363636t + t2 = 0 + 8.636363636 -8.636363636t + t2 = 0 + 8.636363636 Combine like terms: 0 + 8.636363636 = 8.636363636 -8.636363636t + t2 = 8.636363636 The t term is -8.636363636t. Take half its coefficient (-4.318181818). Square it (18.64669421) and add it to both sides. Add '18.64669421' to each side of the equation. -8.636363636t + 18.64669421 + t2 = 8.636363636 + 18.64669421 Reorder the terms: 18.64669421 + -8.636363636t + t2 = 8.636363636 + 18.64669421 Combine like terms: 8.636363636 + 18.64669421 = 27.283057846 18.64669421 + -8.636363636t + t2 = 27.283057846 Factor a perfect square on the left side: (t + -4.318181818)(t + -4.318181818) = 27.283057846 Calculate the square root of the right side: 5.223318662 Break this problem into two subproblems by setting (t + -4.318181818) equal to 5.223318662 and -5.223318662.Subproblem 1
t + -4.318181818 = 5.223318662 Simplifying t + -4.318181818 = 5.223318662 Reorder the terms: -4.318181818 + t = 5.223318662 Solving -4.318181818 + t = 5.223318662 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.318181818' to each side of the equation. -4.318181818 + 4.318181818 + t = 5.223318662 + 4.318181818 Combine like terms: -4.318181818 + 4.318181818 = 0.000000000 0.000000000 + t = 5.223318662 + 4.318181818 t = 5.223318662 + 4.318181818 Combine like terms: 5.223318662 + 4.318181818 = 9.54150048 t = 9.54150048 Simplifying t = 9.54150048Subproblem 2
t + -4.318181818 = -5.223318662 Simplifying t + -4.318181818 = -5.223318662 Reorder the terms: -4.318181818 + t = -5.223318662 Solving -4.318181818 + t = -5.223318662 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.318181818' to each side of the equation. -4.318181818 + 4.318181818 + t = -5.223318662 + 4.318181818 Combine like terms: -4.318181818 + 4.318181818 = 0.000000000 0.000000000 + t = -5.223318662 + 4.318181818 t = -5.223318662 + 4.318181818 Combine like terms: -5.223318662 + 4.318181818 = -0.905136844 t = -0.905136844 Simplifying t = -0.905136844Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.54150048, -0.905136844}
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